Christopher Tisdell

Christopher Tisdell
UNSW Sydney | UNSW · School of Mathematics and Statistics

Doctor of Philosophy
Professor & Chair | Digital Education | STEM Education | Education Industry Advisor | Teacher | Mathematician

About

143
Publications
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Introduction
My contributions to research aim to provide humanity with alternative constructs to work with that illuminate our world in a new way. My research portfolio is of a multidimensional nature, resting on four complementary pillars: 1) mathematics research 2) STEM education research (particularly mathematics education research) 3) Digital education 4) research into higher education.

Publications

Publications (143)
Chapter
For many years, the Australian government has commissioned survey data on multiple facets of the experience of university students in order to improve teaching and learning and its outcomes. Over the last decade, these surveys have reported much lower satisfaction ratings for quality indicators related to feedback/comments provided to students abou...
Article
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For thousands of years, the compass-and-straightedge tools have dominated the learning and teaching of geometry. As such, these inherited, long-standing instruments have gained a lustre of naturalized pedagogical value. However, mounting evidence suggests that many learners and teachers struggle to efficiently, effectively and safely use compasses...
Conference Paper
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"Loneliness, defined as a subjective experience of social isolation, has been identified as the next public health epidemic of the 21st century" (Lim, 2018). When combined with the recent impact of COVID-19 on engineering education, advancing our understanding of belonging and community forms a critical and timely challenge. Mounting evidence point...
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The purpose of this article is to move towards a more complete understanding of the qualitative properties of solutions to discrete boundary value problems. In particular, we introduce and develop sufficient conditions under which the existence of a unique solution for a third-order difference equation subject to three-point boundary conditions is...
Presentation
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Now, more than ever, students are learning mathematics with technology. Mathematics teachers and professors are "becoming digital" in new and relatively radical ways, including within the contexts of delivery, assessment and learning communities. Entire institutions have pivoted to fully online mode of operation due to COVID-19 in a very short amou...
Article
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Recently, Tisdell [48] developed some alternative pedagogical perspectives of multiplication strategies via cut-and-paste actions, underpinned via the principle of conservation of area. However, the ideas therein were limited to problems involving two factors that were close together, and so would not directly apply to a problem such as 17 × 93. Th...
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An alternative pedagogical design is discussed that aims to guide engineering students to solve first-order ordinary differential equations (ODEs), and is based on students’ learning weaknesses identified from previous teaching and learning activities. This approach supported student’s self-enrichment through exploration of relevant resources in OD...
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The purpose of this work is to interpret the experiences of students when audience response systems (ARS) were implemented as a strategy for teaching large mathematics lecture groups at university. Our paper makes several contributions to the literature. Firstly, we furnish a basic model of how ARS can form a teaching and learning strategy. Secondl...
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The purpose of this research is to connect fixed point methods with certain third-order boundary value problems in new and interesting ways. Our strategy involves an analysis of the problem under consideration within closed and bounded sets. We develop sufficient conditions under which the associated mappings will be contractive and invariant in th...
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The purpose of this work is to explore alternative geometric pedagogical perspectives concerning justifications to 'fast' multiplication algorithms in a way that fosters opportunities for skill and understanding within younger, or less algebraically inclined, learners. Drawing on a visual strategy to justify these algorithms creates pedagogical alt...
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The purpose of this work is to move towards a more complete understanding of the roles that shooting methods can play in the theory of discrete boundary value problems. I take the position that shooting methods can have an important function in exploring discrete boundary value problems due to: their mutually compatible characteristics; their acces...
Technical Report
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The HERDSA Fellowship: Rocket to rocket-booster – Chris Tisdell takes us on an interplanetary mentoring journey to Planet FHERDSA
Book
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Major developments in chemistry, molecular cell biology and genetics have enabled a deeper understanding of numerous life processes around us. However, much remains to be explored and revealed. The purpose of this book is to provide a more complete theory of emerging concepts in chemical and biological sciences.
Book
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This edited volume covers a wide range of studies in sustainable development and informatics. It aims to make a note-worthy contribution to the emerging body of knowledge in this important area of global challenge and to influence government and policy makers as a mechanism for changes in practice for a sustainable future. Further, this volume aims...
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The aim of this article is to form a new uniqueness result for a class of initial value problems involving a coupled system of nonlinear Riemann-Liouville fractional differential equations. The main tools involve the Banach contraction principle and the introduction of a new definition of measuring distance in an appropriate normed space. The new r...
Chapter
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For many years, the Australian government has commissioned survey data on multiple facets of the experience of university students in order to improve teaching and learning and its outcomes. Over the last decade, these surveys have reported much lower satisfaction ratings for quality indicators related to feedback/comments provided to students abou...
Conference Paper
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CONTEXT: Online forms of sharing continue to be important within the current disruption of CoViD-19 where it has been necessary to learn and share remotely via digital means. As engineering educators, we have been challenged to adapt quickly to this unusual environment, and one strategy has included the creation and sharing of open educational reso...
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We examine the existence and uniqueness of solutions to two-point boundary value problems involving fourth-order, ordinary differential equations. Such problems have interesting applications to modelling the deflections of beams. We sharpen traditional results by showing that a larger class of problems admit a unique solution. We achieve this by dr...
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The purpose of this article is to construct a firm mathematical foundation for the boundary value problem associated with a generalized Emden equation that embraces Thomas-Fermi-like theories. Boundary value problems for the relativistic and nonrelativistic Thomas-Fermi equations are included as special cases. Questions of existence and uniqueness...
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EMAC 2019 UNSW Canberra, Australia 26th Nov–29th Nov 2019 This Special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 14th Engineering Mathematics and Applications Conference (EMAC2019), which was held at the UNSW Canberra, Australia from 26th November to 29th November 2019. EMAC is held under the auspic...
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The aim of this work is to develop a fuller theory regarding the existence, uniqueness and approximation of solutions to third-order boundary value problems via fixed point methods. To develop this deeper understanding of qualitative properties of solutions, our strategy involves an analysis of the problem under consideration, and its associated op...
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The purpose of this work is to advance the current state of mathematical knowledge regarding fixed point theorems of functions. Such ideas have historically enjoyed many applications , for example, to the qualitative and quantitative understanding of differential, difference and integral equations. Herein, we extend an established result due to Rus...
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The purpose of this note is to sharpen Smirnov's recent work on existence and uniqueness of solutions to third-order ordinary differential equations that are subjected to two-and three-point boundary conditions. The advancement is achieved in the following ways. Firstly, we provide sharp and sharpened estimates for integrals regarding various Green...
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Recently, Lima lamented on the "time consuming and tiresome" pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pen-and-pencil solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula. Drawing o...
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The purpose of this paper is to introduce more general results on the existence of solutions for nonlinear dynamic equations on time scales with impulses and nonlocal initial conditions. We establish the existence of solutions by applying a fixed point result due to O'Regan, while the uniqueness of solutions is obtained through the contraction mapp...
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The aim of this article is to form new existence theory for global solutions to nonlinear fractional differential equations. Traditional approaches to existence, uniqueness and approximation of global solutions for initial value problems involving fractional differential equations have been unwieldy or intractable due to the limitations of previous...
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In this work I examine a case of arts-integrated teaching in mathematics by investigating a piece of lyrics and music. The song under investigation was designed to inspire and explain mathematical concepts of the number e through verse. Through personal reflection, I discuss the inspiration, perspectives and influences in creating the song. I offer...
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Recently, Gauthier introduced a method to construct solutions to the equations of motion associated with oscillating systems into the mathematics education research literature. In particular, Gauthier's approach involved certain manipulations of the differential equations; and drew on the theory of complex variables. Motivated by the work of Gauthi...
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This article analyzes nonlinear, second-order difference equations subject to "left-focal" two-point boundary conditions. Our research questions are: RQ1: What are new, sufficient conditions under which solutions to our "discrete" problem will exist?; RQ2: What, if any, is the relationship between solutions to the discrete problem and solutions o...
Conference Paper
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This case study investigates educational microcontent as an online delivery mechanism for course content, specifically assessing its impact on the subjective student learning experience. Microcontent was introduced as a supplementary resource to students across three Computer Science courses at the University of New South Wales (UNSW). Content was...
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In this work we critically examine a mnemonic designed for the pedagogy of first-order ordinary differential equations. The particular mnemonic takes the form of the SHIELDS acronym. We perform a critical analysis on mnemonics, outlining some of their benefits and limitations from the literature. As a result, we propose a general mnemonic model tha...
Article
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Effective mentoring brings positive outcomes for mentees, mentors and their organizations. Modern mentoring is developing through employment of technology and thus it is important to better understand these new opportunities and their limitations. Termed as “e-mentoring”, the field remains under-researched and sub-optimally theorized. In this work...
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Schoenfeld's work on mathematical thinking and problem-solving in mathematics education is well-known and has been influential for decades. In this note, we examine these models through the lens of exemplification. We aim to provide readers with a useful, tangible perspective by connecting Schoenfeld's models with some particular examples that can...
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In this paper, we are concerned with the existence of mild solution and controllability for a class of nonlinear fractional control systems with damping in Hilbert spaces. Our first step is to give the representation of mild solution for this control system by utilizing the general method of Laplace transform and the theory of (�,)-regularized fami...
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The interest in, and use of, computers and software for assessment is reported to be increasingly popular via electronic examinations (e-exams). We deepen our understanding of the design, reception and effectiveness of e-exams for history and philosophy of science modules, undertaken by first-year advanced science and medical science students at un...
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Recently, Robin claimed to introduce clever innovations (‘wrinkles’) into the mathematics education literature concerning the solutions, and methods of solution, to differential equations. In particular, Robin formulated an iterative scheme in the form of a single integral representation. These ideas were applied to a range of examples involving di...
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Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive approximations...
Article
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Recently, claims of a ‘new and straightforward’ method of solution to second-order linear difference equations have appeared in the mathematics education literature from Rivera-Figueroa and Rivera-Rebolledo. The claim of novelty is based on an assumption that ‘since the equation is worked in its canonical form’, the method within this context must...
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Gronwall’s inequality plays an important role in producing new research and in the learning and teaching of differential and integral equations. The purpose of this work is to advance and simplify the current state of knowledge and pedagogical approaches regarding Gronwall’s inequality. In particular: we extend known versions of Gronwall’s inequali...
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We consider an initial value problem involving a single-term Caputo fractional differential equation. For those with right-hand sides that satisfy the Osgood condition, we establish novel uniqueness and comparison theorems.In addition, we discuss a reduction of the fractional order problem to an integer-ordered one. We identify inconsistencies in r...
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This paper is based on the presumption that teaching multiple ways to solve the same problem has academic and social value. In particular, we argue that such a multifaceted approach to pedagogy moves towards an environment of more inclusive and personalized learning. From a mathematics education perspective, our discussion is framed around pedagogi...
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The aim of this article is to establish sufficient conditions for the approximate controllability of fractional control systems with time delay in Hilbert spaces. By the technique of sequential approach, we prove that the fractional control systems with time delay are approximately controllable. Finally, an example is provided to illustrate our...
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The purpose of this work is to advance and simplify our under-standing of some of the basic theory of linear dynamic equations and dynamic inequalities on time scales.Firstly, we revisit and simplify approaches to Gronwall’s inequality on timescales. We provide new, simple and direct proofs that are accessible to those with only a basic understandi...
Conference Paper
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Motivated by the need for more clarity in openness in education, this paper aims to add to the theoretical basis that underpins our ideas of openness. A range of simple models for openness are introduced together with some critical perspectives regarding them. The discussions are grounded within the theories of: scientific model building; semantics...
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This paper presents some critical perspectives regarding pedagogical approaches to the method of reversing the order of integration in double integrals from prevailing educational literature on multivariable calculus. First, we question the message found in popular textbooks that the traditional process of reversing the order of integration is nece...
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For over 50 years, the learning of teaching of a priori bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to a priori bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving second-order, linear problems wit...
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Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching ‘well posedness’ of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order sy...
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We produce new global existence and uniqueness results for solutions to systems of initial value problems involving fractional differential equations. The uniqueness results rely on differential inequalities and a comparison with monotonically converging sequences of functions. The existence results involve fixed-point theorems that rely on a strat...
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Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem thro...
Conference Paper
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CONTEXT As the popularity of blended and online learning continues to grow in higher education, the role of the engineering educator will continue to change for developing the future engineer. Over the past 10 years there has been a worldwide shift by educators to use online educational video to enhance student learning of course material. However,...
Conference Paper
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As universities have transitioned from paper to online student evaluations, concerns have been raised regarding falling or low survey participation rates. We report on our recent study that explored how blended survey methods could increase participation rates in online student surveys. At the heart of our methods was the use of personal devices by...
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Closed captioning of instructional videos is a topic that has not seen much discussion despite its importance for hearing-impaired students and recent legal ramifications if videos are not appropriately captioned. In particular, it is unclear what best practice in captioning videos should be to benefit all learners in disciplines such as mathematic...
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This article investigates nonlinear, second-order ordinary differential equations subject to various two-point boundary conditions. A condition is introduced that ensures a priori bounds on the derivatives of solutions to the problem. In particular, quadratic growth conditions on the right-hand side of the differential equation are not employed. Th...
Conference Paper
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This work reports on a case study on how employability skills can be embedded within science, mathematics and medical science students. The cohort involved two courses within three programs and almost 500 first-year students at a large, research-intensive university. The approach was to redesign the curriculum within these courses to form a T-shape...
Article
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We investigate two types of first-order, two-point boundary value problems (BVPs). Firstly, we study BVPs that involve nonlinear difference equations (the “discrete” BVP); and secondly, we study BVPs involving nonlinear ordinary differential equations (the “continuous” BVP). We formulate some sufficient conditions under which the discrete BVP will...
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This article examines the qualitative properties of solutions to systems of boundary value problems involving fractional differential equations. Our primary interest is in forming new results that involve sufficient conditions for the existence of solutions. To do this, we formulate some new ideas concerning a priori bounds on solutions, which are...
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When do fractional differential equations have solutions on the half line that are bounded by the Mittag-Leffler function? This work answers the above question through fixed-point methods, providing a deeper understanding of the long term growth behaviour of solutions, in addition to advancing our knowledge on the existence and uniqueness of soluti...
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This article presents a firm mathematical foundation for the boundary value problem associated with the nonrelativistic Thomas–Fermi equation for heavy atoms in intense magnetic fields. Our approach uses an application of differential inequalities and ideas from nonlinear analysis, including: the technique of lower and upper solutions;and fixed–poi...
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This article examines two-point boundary value problems (BVPs) for second-order, singular ordinary differential equations where the right-hand-side of the differential equation may depend on the derivative of the solution. We introduce a method to obtain a priori bounds on all potential solutions, including their “derivatives”, to the singular BVP...
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This note discusses the question: When do nonlinear fractional differential equations of arbitrary order have solutions that extend to a maximal interval of existence? We show that a growth condition on the right-hand side of the equation ensures that solutions will extend. The method uses a classical approach from analysis, namely the divergence o...
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This work investigates a two-point boundary value problem (BVP) involving a first-order difference equation, known as the 'discrete' BVP. Some sufficient conditions are formulated under which the discrete BVP will possess a unique solution. The innovation herein involves a strategic choice of metric and utilization of Hölder's inequality. This appr...
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This article analyzes qualitative properties of solutions to two-point boundary value problems for singular ordinary differential equations. In particular, we form new approaches that ensure that all possible solutions satisfy certain a priori bounds. The methods involve differential inequalities.The ideas are then applied to generate new existence...
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This article analyzes the existence and approximation of solutions to initial value problems for nonlinear fractional differential equations of arbitrary order. Several new approaches are furnished in the environment of fractional differential equations, such as the sequential technique of Cauchy-Peano and the Leray-Schauder topological degree. In...
Article
In this work we analyse a nonlinear, second-order difference equation on an unbounded interval. We present new conditions under which the problem admits a unique solution that is of a particular linear asymptotic form. The results concern the general behaviour of solutions to the initial-value problem, as well as solutions with a given asymptote. O...
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In this paper, we study the existence of multiple solutions of boundary value problems for second-order discrete equations , , , bounded on . The proofs are based on the upper and lower solutions, degree theory and sequential argument.
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We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis on $\R$ to a new form for difference equations, quantum equations, and arbitrary dynamic equations on time sc...
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We are interested in the exponential stability of the zero solution of a functional dynamic equation on a time scale, a nonempty closed subset of real numbers. The approach is based on suitable Lyapunov functionals and certain inequalities. We apply our results to obtain exponential stability in Volterra integrodynamic equations on time scales.
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The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, an...
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Many dynamical systems have an impulsive dynamical behavior due to abrupt changes at certain instants during the evolution process. The mathematical description of these phenomena leads to impulsive differential equations. In this work, we present some new results concerning the exact controllability of a nonlinear ordinary differential equation wi...
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Using the method of upper and lower solutions, we prove that the singular boundary value problem, \[ -u'' = f(u) ~ u^{-\alpha} \quad \textrm{in} \quad (0, 1), \quad u'(0) = 0 = u(1) \, , \] has a positive solution when $0 < \alpha < 1$ and $f : \mathbb{R} \to \mathbb{R}$ is an appropriate nonlinearity that is bounded below; in particular, we allow...
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This article considers the Dirichlet problem of homogeneous and inhomoge-neous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the no...
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In this paper we establish the method of successive approximations within the field of "dynamic equations on time scales". Our introduction and application of the method leads to new results concerning the qualitative and quantitative properties of solutions to nonlinear dynamic equations on time scales. The new discoveries include sufficient condi...
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In this paper, we deal with the existence of at least three classical solutions for the following two point boundary value problem {(phi(p)(u '))' + lambda f(t,u) = 0, alpha(1)u(a) - alpha(2)u '(a) = 0, beta(1)u(b) + beta(2)u '(b) = 0, where phi(p) (s) = |s|(p-2)s, p > 1 is a constant, lambda is a positive parameter, a, b epsilon R, a < b. Our main...
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We establish some new sufficient conditions under which periodic and non-periodic solutions exist for systems of nonlinear, first-order differential inclusions.Our new results are significant for two main reasons: they apply to differential inclusions that may have a right-hand side that grows super-linearly in the second variable and thus our idea...
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This article investigates both basic qualitative and basic quantitative properties of solutions to first- and higher-order dynamic equations on time scales and thus provides a foundation and framework for future advanced nonlinear studies in the field. Particular focus lies in the: existence; uniqueness; dependency; approximation; and explicit repr...
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In this paper we examine "terminal" value problems for dynamic equations on time scales - that is, a dynamic equation whose solutions are asymptotic at infinity. We present a number of new theorems that guarantee the existence and uniqueness of solutions, as well as some comparison-type results. The methods we employ feature dynamic inequalities, w...
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This article introduces the basic qualitative and basic quantitative theory of Volterra integral equations on time scales and thus may be considered as a foundation for future advanced studies in the field. New sufficient conditions are introduced that guarantee: existence; uniqueness; approximation; boundedness and certain growth rates of solution...
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This paper presents some new results for the existence of a unique 2 -periodic solution of even order dieren tial equations. Here the assumption in [3, J. H. Chen and D. O’Regan, On periodic solutions for even order dieren tial equations, Nonlinear Anal., (2007), doi: 10.1016/j.na.2007.06.013] that maximal solution of an initial value problem exist...
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We consider the generalization of two classical periodic problems to the context of time scales. On the one hand, we generalize a celebrated result by A. Castro [Differential equations, Proc. 8th Fall Conf., Okla. State Univ. 1979, 149–160 (1980; Zbl 0569.34039)] for the forced pendulum equation. On the other hand, we extend a well-known result by...
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This paper focuses on the qualitative and quantitative properties of solutions to certain nonlinear dynamic equations on time scales. We present some new sufficient conditions under which these general equations admit a unique, positive solution. These positive (and hence non–oscillatory) solutions: extend across unbounded intervals; and tend to a...
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This article analyzes the solvability of second-order, nonlinear dynamic boundary value problems (BVPs) on time scales. New Bernstein-Nagumo conditions are developed that guarantee an a priori bound on the delta derivative of potential solutions to the BVPs under consideration. Topological methods are then employed to gain solvability. Key words: B...
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We establish existence results for multiple solutions to boundary value problems for nonlinear, second order, ordinary differential equations subject to nonlinear boundary conditions involving two points. We apply our theory to a problem from chemical reactor theory. Our results are extended to systems of equations.
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In this work we present some new results concerning the existence and uniqueness of solutions to an impulsive first-order, nonlinear ordinary differential equation with "non-periodic" boundary conditions. These boundary conditions include, as a special case, so-called "anti-periodic" boundary conditions. Our methods to prove the existence and uniqu...
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We gain solvability of a system of nonlinear, second-order ordinary differential equations subject to a range of boundary conditions. The ideas involve differential inequalities and fixed point methods. In particular, maximum principles are not employed.
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We consider the following system of Volterra intergral equations ui(t )= Z t 0 gi(t,s)(fi(s,u1(s),u2(s),···,un(s)) + hi(s,u1(s),u2(s),···,un(s)))ds, t 2 (0,T), 1 i n and some of its particular cases that arise from physical problems. Criteria are oered for the existence of one and more constant-sign solutions u =( u1,u2,···,un) of the system in (C(...
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In this work we obtain some new results concerning the existence of solutions to an impulsive first-order, nonlinear ordinary differential equation with periodic boundary conditions. The ideas involve differential inequalities and Schaefer's fixed-point theorem.
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In this article we gain solvability to a nonlinear, second-order difference equation with discrete Neumann boundary conditions. Our methods involve new inequalities on the right-hand side of the difference equation and Schaefer's Theorem in the finite-dimensional space setting.
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Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary differential inclusions. Some new Bernstein–Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjun...
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Oscillation and nonoscillation properties of second order Sturm{Liouville dynamic equations on time scales attracted much interest. These equations include, as special cases, second order self-adjoint dierential equations as well as second order Sturm{Liouville dierence equations. In this paper we con- sider a given (homogeneous) equation and a cor...
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We are concerned with the existence and form of positive solutions to a nonlinear third-order three-point nonlocal boundary-value problem on general time scales. Using Green's functions, we prove the existence of at least one positive solution using the Guo-Krasnoselskii fixed point theorem. Due to the fact that the nonlinearity is allowed to chang...
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Using variational methods we study the generalization of two classical second order periodic problems in the context of time scales. On the one hand, we study a forced pendulum-type equation. On the other hand, we obtain solutions for a bounded nonlinearity under Landesman–Lazer type conditions.
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This article analyzes a nonlinear system of first-order difference equations with periodic and non-periodic boundary conditions. Some sufficient conditions are presented under which: potential solutions to the equations will satisfy certain a priori bounds; and the equations will admit at least one solution. The methods involve new dynamic inequali...
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This article investigates the existence of solutions to boundary value problems (BVPs) involving systems of first-order ordinary differential equations and two-point, periodic boundary conditions. The methods involve novel differential inequalities and fixed-point theory to yield new theorems guaranteeing the existence of at least one solution.
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This paper investigates the solvability of discrete Dirichlet boundary value prob-lems by the lower and upper solution method. Here, the second order difference equation with a nonlinear right hand side f is studied and f (t, u, v) can have a su-perlinear growth both in u and in v. Moreover, the growth conditions on f are one-sided. We compute a pr...
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This article investigates the existence of solutions to first-order nonlinear boundary-value problems (BVPs) involving systems of ordinary differential equations and two-point boundary conditions. Some sufficient conditions are presented that will ensure solvability. The main tools employed are novel differential inequalities and fixed-point method...

Projects

Projects (8)
Project
To develop new existence results for fractional differential equations via fixed point Theory.
Project
My contributions to educational research aim to provide alternative constructs for humanity to work with that illuminate our world in a new way.
Project
My contributions to research in differential inclusions aim to provide alternative constructs for humanity to work with that illuminate our world in a new way.