Sheng-Da Zeng

Sheng-Da Zeng
Jagiellonian University | UJ · Faculty of Mathematics and Computer Science

Phd

About

112
Publications
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1,659
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October 2013 - May 2016
Guangxi University for Nationalities
Position
  • Research Director

Publications

Publications (112)
Article
In this paper we introduce the differential system obtained by mixing an evolution equation and a variational inequality ((EEVI), for short). First, by using KKM theorem and monotonicity arguments, we prove the superpositional measurability and upper semicontinuity for the solution set of a general variational inequality. Then we establish that the...
Article
In this paper we study a class of hyperbolic variational inequalities without a term depending on the first order derivative. Results on existence, uniqueness and regularity of a solution to the variational inequality are provided through the Rothe method. A frictional dynamic contact problem for viscoelastic material with noncoercive viscosity and...
Article
In this paper a class of elliptic hemivariational inequalities involving the time-fractional order integral operator is investigated. Exploiting the Rothe method and using the surjectivity of multivalued pseudomonotone operators, a result on existence of solution to the problem is established. Then, this abstract result is applied to provide a theo...
Article
In this paper, we firstly introduce a complicated system obtained by mixing a nonlinear evolutionary partial differential equation and a mixed variational inequality in infinite dimensional Banach spaces in the case where the set of constraints is not necessarily bounded and the problem is driven by nonlocal boundary conditions, which is called par...
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The aim of this paper is to introduce and study a new class of problems called partial differential hemivariational inequalities that combines evolution equations and hemivariational inequalities. First, we introduce the concept of strong well-posedness for mixed variational quasi hemivariational inequalities and establish metric characterizations...
Article
We consider a nonlinear Dirichlet problem driven by the anisotropic (p,q)-Laplacian and a Carathéodory reaction f(z,x) locally defined in x. Using critical point theory, truncation and comparison techniques as well as critical groups, we show the existence of at least three nontrivial smooth solutions (positive, negative and nodal). If a symmetry c...
Article
This paper is devoted to the study of the L∞-bound of solutions to the double-phase nonlinear problem with variable exponent by the case of a combined effect of concave–convex nonlinearities. The main tools are the De Giorgi iteration method and a truncated energy technique. Applying this and a variant of Ekeland’s variational principle, we give th...
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This paper is devoted to the development and analysis of a pressure projection stabilized mixed finite element method, with continuous piecewise linear approximations of velocities and pressures, for solving a hemivariational inequality of the stationary Stokes equations with a nonlinear non-monotone slip boundary condition. We present an existence...
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In this paper, some novel conditions for the stability results for a class of fractional-order quasi-linear impulsive integro-differential systems with multiple delays is discussed. First, the existence and uniqueness of mild solutions for the considered system is discussed using contraction mapping theorem. Then, novel conditions for Mittag–Leffle...
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We study a nonlinear evolutionary quasi–variational–hemivariational inequality (in short, (QVHVI)) involving a set-valued pseudo-monotone map. The central idea of our approach consists of introducing a parametric variational problem that defines a variational selection associated with (QVHVI). We prove the solvability of the parametric variational...
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In this paper, we introduce and investigate a new kind of coupled systems, called coupled variational inequalities, which consist of two elliptic mixed variational inequalities on Banach spaces. Under general assumptions, by employing Kakutani-Ky Fan fixed point theorem combined with Minty technique, we prove that the set of solutions for the coupl...
Article
In this paper, we consider a Dirichlet problem driven by the anisotropic (p, q)-Laplacian and a superlinear reaction which need not satisfy the Ambrosetti–Robinowitz condition. By using variational tools together with truncation and comparison techniques and critical groups, we show the existence of at least five nontrivial smooth solutions, all wi...
Article
In this paper, we investigate a nonlinear and nonsmooth dynamics system (NNDS, for short) involving two multi-valued maps which are a convex subdifferential operator and a generalized subdifferential operator in the sense of Clarke, respectively. Under general assumptions, by using a surjectivity theorem for multi-valued mappings combined with the...
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The primary goal of this paper is to study a nonlinear complementarity system (NCS, for short) with a nonlinear and nonhomogeneous partial differential operator and mixed boundary conditions, and a simultaneous distributed-boundary optimal control problem governed by (NCS), respectively. First, we formulate the weak formulation of (NCS) to a mixed...
Article
This paper investigates the inverse problem of estimating a discontinuous parameter in a quasi-variational inequality involving multi-valued terms. We prove that a well-defined parameter-to-solution map admits weakly compact values under some quite general assumptions. The Kakutani-Ky Fan fixed point principle for multi-valued maps is the primary t...
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In this paper, a nonlinear elliptic obstacle problem is studied. The nonlinear nonhomogeneous partial differential operator generalizes the notions of p -Laplacian while on the right hand side we have a multivalued convection term (i.e., a multivalued reaction term may depend also on the gradient of the solution). The main result of the paper provi...
Article
In this article, we study a large class of evolutionary variational–hemivariational inequalities of hyperbolic type without damping terms, in which the functional framework is considered in an evolution triple of spaces. The inequalities contain both a convex potential and a locally Lipschitz superpotential. The results on existence, uniqueness, an...
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We consider a parametric nonlinear, nonhomogeneous Dirichlet problem driven by the ( p , q )-Laplacian with a reaction involving a singular term plus a superlinear reaction which does not satisfy the Ambrosetti–Rabinowitz condition. The main goal of the paper is to look for positive solutions and our approach is based on the use of variational tool...
Article
In this paper, we consider a mixed boundary value problem with a double phase partial differential operator, an obstacle effect and a multivalued reaction convection term. Under very general assumptions, an existence theorem for the mixed boundary value problem under consideration is proved by using a surjectivity theorem for multivalued pseudomono...
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The goal of this paper is to investigate a new class of elliptic mixed boundary value problems involving a nonlinear and nonhomogeneous partial differential operator [Formula: see text]-Laplacian, and a multivalued term represented by Clarke’s generalized gradient. First, we apply a surjectivity result for multivalued pseudomonotone operators to ex...
Article
The term fractional differentiation has recently been merged with the term fractal differentiation to create a new fractional differentiation operator. Several kernels were used to explore these new operators, including the power-law, exponential decay, and Mittag-Leffler functions. In this study, we analyze three forms of interpersonal relationshi...
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In this paper, we propose a new methodology to study evolutionary variational-hemivariational inequalities based on the theory of evolution equations governed by maximal monotone operators. More precisely, the proposed approach, based on a hidden maximal monotonicity, is used to explore the well-posedness for a class of evolutionary variational-hem...
Article
We consider a hemivariational inequality of elliptic type (HVI, for short) in a reflexive Banach space, prove its solvability and the compactness of its set of solutions. To this end we employ a surjectivity theorem for multivalued mappings that we use for the sum of a maximal monotone operator and a bounded pseudomonotone operator. Next, we introd...
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This paper is devoted the study of a generalized hybrid dynamical system, which consists of a history-dependent hemivariational inequality of parabolic type and a nonlinear evolution equation. The unique solvability for the system is established via applying surjectivity of multivalued pseudomonotone operators, fixed point theorem, and properties o...
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The primary objective is to investigate a class of noncoercive variational–hemivariational inequalities on a Banach space. We start with several new existence results for the abstract inequalities in which our approach is based on arguments of recession analysis and the theory of pseudomonotone operators. A nonsmooth elastic contact problem is cons...
Article
We consider a history-dependent variational–hemivariational inequality with unilateral constraints in a reflexive Banach space. The unique solvability of the inequality follows from an existence and uniqueness result obtained in Sofonea and Migórski (2016, 2018). In this current paper we introduce and study a generalized penalty method associated t...
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In this paper, we consider a thermoelastic contact problem in which the heat exchange boundary condition is affected by normal displacement on contact boundary, and the operator in the nonlinear thermoelastic constitutive law is considered to rely on temperature field. First, we deliver the weak formulation of the thermoelastic contact problem whic...
Preprint
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In this paper we consider a mixed boundary value problem with a nonhomogeneous, nonlinear differential operator (called double phase operator), a nonlinear convection term (a reaction term depending on the gradient), three multivalued terms and an implicit obstacle constraint. Under very general assumptions on the data, we prove that the solution s...
Article
In the present paper, we consider a nonlinear Robin problem driven by a nonhomogeneous differential operator and with a reaction which is only locally defined. Using cut-off techniques and variational tools, we show that the problem has a sequence of nodal solutions converging to zero in C 1 ( Ω ‾ ).
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The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition, and nonmonotone multivalued contact, and friction laws of subdifferential form. First, under suitable assumpt...
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We consider a nonlinear Dirichlet problem driven by the (p, q)-Laplacian and with a reaction which is dependent on the gradient. We look for positive solutions and we do not assume that the reaction is nonnegative. Using a mixture of variational and topological methods (the "frozen variable" technique), we prove the existence of a positive smooth s...
Preprint
Full-text available
In this paper, we consider a mixed boundary value problem with a double phase partial differential operator, an obstacle effect and a multivalued reaction convection term. Under very general assumptions, an existence theorem for the mixed boundary value problem under consideration is proved by using a surjectivity theorem for multivalued pseudomono...
Article
The aim of this paper is to study an elliptic bilateral obstacle system (EBOS, for short) involving a nonlinear and nonhomogeneous partial differential operator and a multivalued term which is described by Clarke’s generalized gradient. First, we obtain the weak formulation of (EBOS) which is a variational-hemivariational inequality, and prove the...
Article
The goal of this paper is to study an evolution inclusion problem with fractional derivative in the sense of Caputo, and Clarke’s subgradient. Using the temporally semi-discrete method based on the backward Euler difference scheme, we introduce a discrete approximation system of elliptic type corresponding to the fractional evolution inclusion prob...
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In this paper, we study an elliptic obstacle problem with a generalized fractional Laplacian and a multivalued operator which is described by a generalized gradient. Under quite general assumptions on the data, we employ a surjectivity theorem for multivalued mappings generated by the sum of a maximal monotone multivalued operator and a bounded mul...
Article
The aim of this paper is to study a comprehensive dynamics system called fractional fuzzy differential variational inequality, which is composed of a nonlinear fractional differential equation with Atangana-Baleanu fractional derivative and a time-dependent fuzzy variational inequality. We explore an existence and uniqueness theorem for the dynamic...
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The goal of this paper is to study a comprehensive system called differential variational–hemivariational inequality which is composed of a nonlinear evolution equation and a time-dependent variational–hemivariational inequality in Banach spaces. Under the general functional framework, a generalized existence theorem for differential variational–he...
Article
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In the present paper, we introduce a family of the approximating problems corresponding to an elliptic obstacle problem with a double phase phenomena and a multivalued reaction convection term. Denoting by 𝓢 the solution set of the obstacle problem and by 𝓢 n the solution sets of approximating problems, we prove the following convergence relation $...
Article
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The paper is devoted to a new kind of implicit obstacle problem given by a fractional Laplacian-type operator and a set-valued term, which is described by a generalized gradient. An existence theorem for the considered implicit obstacle problem is established, using a surjectivity theorem for set-valued mappings, Kluge’s fixed point principle and n...
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In this paper we investigate the gap functions and regularized gap functions for a class of variational–hemivariational inequalities of elliptic type. First, based on regularized gap functions introduced by Yamashita and Fukushima, we establish some regularized gap functions for the variational–hemivariational inequalities. Then, the global error b...
Article
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In this paper we study implicit obstacle problems driven by a nonhomogenous differential operator, called double phase operator, and a multivalued term which is described by Clarke’s generalized gradient. Based on a surjectivity theorem for multivalued mappings, Kluge’s fixed point principle and tools from nonsmooth analysis, we prove the existence...
Article
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Fractional integral inequality plays a significant role in pure and applied mathematics fields. It aims to develop and extend various mathematical methods. Therefore, nowadays we need to seek accurate fractional integral inequalities in obtaining the existence and uniqueness of the fractional methods. Besides, the convexity theory plays a concrete...
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This paper is devoted to the study of a new class of implicit state-dependent sweeping processes with history-dependent operators. Based on the methods of convex analysis, we prove the equivalence of the history/state dependent implicit sweeping process and a nonlinear differential equation, which, through a fixed point argument for history-depende...
Article
The aim the paper is to study a large class of variational-hemivariational inequalities involving constraints in a Banach space. First, we establish a general existence theorem for this class. Second, we introduce a sequence of penalized problems without constraints. Under the suitable assumptions, we prove that the Kuratowski upper limit with resp...
Article
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Two significant inequalities for generalized time fractional derivatives at extreme points are obtained. Then, we apply the inequalities to establish the maximum principles for multi-term time-space fractional variable-order operators. Finally, we employ the principles to investigate two kinds of diffusion equations involving generalized time-fract...
Article
The paper sets forth a new type of variational problem without any ellipticity or monotonicity condition. A prototype is a differential inclusion whose driving operator is the competing weighted $(p,q)$-Laplacian $-\Delta_p u+\mu\Delta_q u$ with $\mu\in \mathbb{R}$. Local and nonlocal boundary value problems fitting into this nonstandard setting ar...
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During the last years several fractional integrals were investigated. Having this idea in mind, in the present article, some new generalized fractional integral inequalities of the trapezoidal type for k u-preinvex functions, which are differentiable and twice differentiable, are established. Then, by employing those results, we explore the new est...
Article
The aim of the paper is to introduce and investigate a dynamical system which consists of a variational–hemivariational inequality of hyperbolic type combined with a non-linear evolution equation. Such a dynamical system arises in studies of complicated contact problems in mechanics. Existence, uniqueness and regularity of a global solution to the...
Article
The goal of this paper is to investigate a parametric Dirichlet problem with (p,q)-Laplacian and concave–convex nonlinearity. Denoting by Sλ the set of positive solutions of the problem corresponding to the parameter λ>0, we prove that the set Sλ is compact in the W01,p(Ω)-topolgy. We also establish an upper semicontinuity and a Mosco convergence r...
Article
The main goal of this paper is the study of an elliptic obstacle problem with a double phase phenomena and a multivalued reaction term which also depends on the gradient of the solution. Such term is called multivalued convection term. Under quite general assumptions on the data, we prove that the set of weak solutions to our problem is nonempty, b...
Article
In this paper, we study a class of generalized and not necessarily differentiable functionals of the form [Formula: see text] with functions [Formula: see text], [Formula: see text] that are only locally Lipschitz in the second argument and involving critical growth for the elements of their generalized gradients [Formula: see text] even on the bou...
Article
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The purpose of this work is to introduce and investigate a complicated variational–hemivariational inequality of parabolic type with history-dependent operators. First, we establish an existence and uniqueness theorem for a first-order nonlinear evolution inclusion problem, which is driven by a convex subdifferential operator for a proper convex fu...
Article
We investigate a generalized Lagrange multiplier system in a Banach space, called a mixed variational–hemivariational inequality (MVHVI, for short), which contains a hemivariational inequality and a variational inequality. First, we employ the Minty technique and a monotonicity argument to establish an equivalence theorem, which provides three diff...
Article
The paper is devoted to investigate a new kind of variational-hemivariational inequality of parabolic type driven by a generalized space-fractional Laplace operator, and two multivalued terms which are expressed by the Clarke generalized gradient and convex subgradient, respectively. An existence theorem of weak solutions to the problem is establis...
Article
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This paper is devoted to a generalized evolution system called fractional partial differential variational inequality which consists of a mixed quasi-variational inequality combined with a fractional partial differential equation in a Banach space. Invoking the pseudomonotonicity of multivalued operators and a generalization of the Knaster-Kuratows...
Article
In this paper we continue the study on generalized mixed variational–hemivariational inequalities which has been recently carried out in Bai et al. (2019). There, several abstract results on existence, uniqueness, and stability of solution are established. To illustrate the applicability of these results, we present two applications. The first appl...
Article
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In this paper, an abstract evolutionary hemivariational inequality with a history-dependent operator is studied. First, a result on its unique solvability and solution regularity is proved by applying the Rothe method. Next, we introduce a numerical scheme to solve the inequality and derive error estimates. We apply the results to a quasistatic fri...
Preprint
First, we consider a new class of convex functions, called σ-convex functions. We obtain new integral inequalities of Hermite-Hadamard type for σ-convex functions with respect to increasing functions via Riemann-Liouville fractional integrals. Our results generalize some existing inequalities involving classical integrals and Riemann-Liouville frac...
Article
The purpose of this paper is to investigate a class of differential variational inequalities involving a constraint set in Banach spaces. A well-posedness result for the inequality is obtained, including the existence, uniqueness, and stability of the solution in mild sense. Further, we introduce a penalized problem without constraints and prove th...
Article
The purpose of this paper is to investigate a class of generalized mixed hemivariational–variational inequalities of elliptic type in a Banach space. A well-posedness result for the inequality is obtained, including existence, uniqueness, and stability of solution. The approach is based on a set-valued fixed point theorem combined with the theory o...
Article
In this paper a class of generalized differential variational inequalities with constraints involving history-dependent operators in Banach spaces is investigated. The unique solvability and regularity results are obtained via surjectivity of multivalued pseudomonotone operators combined with a fixed point principle. From abstract results, a theore...
Article
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The goal of the note is to introduce a new modified subgradient extragradient algorithm for solving variational inequalities in Hilbert spaces. A result on the strong convergence of the algorithm is proved without the knowledge of Lipschitz constant of the operator. Several numerical experiments for the proposed algorithm are presented.
Preprint
We investigate a generalized Lagrange multiplier system in a Banach space, called a mixed variational-hemivariational inequality (MVHVI, for short), which contains a hemivariational inequality and a variational inequality. First, we employ the Minty technique and a monotonicity argument to establish an equivalence theorem, which provides three diff...
Article
Full-text available
This paper is devoted to the study of a class of sweeping processes with history-dependent operators. A well-posedness result is obtained, including the existence, uniqueness, and stability of the solution. Our approach is based on the variable time step-length discrete approximation method combined with a fixed point principle for history-dependen...
Article
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In this paper we study from a qualitative point of view the nonlinear singular Dirichlet problem depending on a parameter λ > 0 that was considered in [32]. Denoting by S λ the set of positive solutions of the problem corresponding to the parameter λ , we establish the following essential properties of S λ : there exists a smallest element $\begin{...
Article
The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is es...
Article
Hemivariational inequalities have been successfully employed for mathematical and numerical studies of application problems involving nonsmooth, nonmonotone and multivalued relations. In recent years, error estimates have been derived for numerical solutions of hemivariational inequalities under additional solution regularity assumptions. Since the...
Preprint
Full-text available
In this paper an abstract evolutionary hemivariational inequality with a history-dependent operator is studied. First, a result on its unique solvability and solution regularity is proved by applying the Rothe method. Next, we introduce a numerical scheme to solve the inequality and derive error estimates. We apply the results to a quasistatic fric...
Preprint
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The primary objective of this research is to investigate an inverse problem of parameter identification in nonlinear mixed quasi-variational inequalities posed in a Banach space setting. By using a fixed point theorem, we explore properties of the solution set of the considered quasi-variational inequality. We develop a general regularization frame...
Article
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The primary objective of this research is to investigate an inverse problem of parameter identification in nonlinear mixed quasi-variational inequalities posed in a Banach space setting. By using a fixed point theorem, we explore properties of the solution set of the considered quasi-variational inequality. We develop a general regularization frame...
Article
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In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution set. Our approach is based on Leray–Schauder alternative principle, method of sub-supersolution, nonlinear regul...
Article
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In this paper we investigate an abstract system which consists of a hemivariational inequality of parabolic type combined with a nonlinear evolution equation in the framework of an evolution triple of spaces which is called a differential hemivariational inequality [(DHVI), for short]. A hybrid iterative system corresponding to (DHVI) is introduced...
Article
In this paper we study a class of multi-term time fractional integral diffusion equations. Results on existence, uniqueness and regularity of a strong solution are provided through the Rothe method. Several examples are given to illustrate the applicability of main results.
Article
In this paper, we provide results on existence, uniqueness and convergence for a class of variational‐hemivariational inequalities of elliptic type involving a constraint set and a nondifferentiable potential. We introduce a penalized and regularized problem without constraints and with Gteaux differentiable potential. We prove that the solution to...
Preprint
Please cite this article in press as: S.D. Zeng, Z.H. Liu, S. Migorski, Positive solutions to nonlinear nonhomogeneous inclusion problems with dependence on the gradient, (2018), https://doi.org/10.1016/j.jmaa.2018.03.033 Abstract. The goal of the paper is to study a generalized elliptic inclusion problem driven by a nonhomogeneous partial differe...
Article
A system which couples an abstract hemivariational inequality of hyperbolic type and an evolution equation in a Banach space is studied. The global existence of the system is established by exploiting the Rothe method. An application to a dynamic adhesive viscoelastic contact problem with friction is provided for which results on existence and regu...
Article
Full-text available
In this paper, we study a class of generalized differential hemivariational inequalities of parabolic type involving the time fractional order derivative operator in Banach spaces. We use the Rothe method combined with surjectivity of multivalued pseudomonotone operators and properties of the Clarke generalized gradient to establish existence of so...
Article
In this paper we investigate the system obtained by mixing a nonlinear evolutionary equation and a mixed variational inequality ((EEVI), for short) on Banach spaces in the case where the set of constraints is not necessarily compact and the problem is driven by a ϕ-pseudomonotone operator which is not necessarily monotone. In this way, we extend th...
Article
This paper is concerned with a numerical method for solving generalized fractional differential equation of Caputo–Katugampola derivative. A corresponding discretization technique is proposed. Numerical solutions are obtained and convergence of numerical formulae is discussed. The convergence speed arrives at O(ΔT1−α). Numerical examples are given...
Article
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This paper is devoted to the study of the differential systems in arbitrary Banach spaces that are obtained by mixing nonlinear evolutionary equations and generalized quasi-hemivariational inequalities (EEQHVI). We start by showing that the solution set of the quasi-hemivariational inequality associated to problem EEQHVI is nonempty, closed, and co...
Article
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We discuss the well-posedness and the well-posedness in the generalized sense of differential mixed quasi-variational inequalities ((DMQVIs), for short) in Hilbert spaces. This gives us an outlook to the convergence analysis of approximating sequences of solutions for (DMQVIs). Using these concepts we point out the relation between metric character...
Article
This paper is devoted to introduce and study a new class of generalized vector complementarity problems ((GVCP), for short) and generalized vector variational inequalities ((GVVI), for short) in fuzzy environment. Under suitable conditions, we prove the equivalence between (GVCP) and (GVVI) in Banach spaces. Then, without any monotonicity assumptio...