# P. K. PalamidesUniversity of Ioannina | UOI · Department of Mathematics

P. K. Palamides

## About

54

Publications

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413

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Citations since 2017

## Publications

Publications (54)

A third-order three-point boundary value problem (BVP) is studied, through this work. We derive sufficient conditions that guarantee the positivity of the solution of the corresponding linear boundary value problem (see Proposition 2). Then, based on the classical Guo-Krasnoselskii fixed point theorem, we obtain positive solutions of the nonlinear...

Using an elementary approach, we prove the existence of three positive and concave solutions of the second-order two-point boundary-value problem
$$ \begin{array}{lll}&& x^{\prime\prime}(t)=\alpha(t)f(t,x(t),x^{\prime}(t)),\qquad 0 < t < 1,\\&& \qquad \qquad \qquad x(0)=x(1)=0.\end{array}$$
We rely on the analysis of the corresponding vector field...

We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive) Green's function, the obtained solution is still of definite sign. Furthermore, we prove the existence of an entire contin...

Using barrier strip arguments, we investigate the existence of C 2 [ 0 , 1 ] -solutions to the Neumann boundary value problem f ( t , x , x ′ , x ′ ′ ) = 0 , x ′ ( 0 ) = a , x ′ ( 1 ) = b .
MSC: 34B15.

We consider the five-point boundary value problem for a fifth-order differential equation, where the nonlin-earity is superlinear at both the origin and +infinity. Our method of proof combines the Kneser's theorem with the well-known from combinatorial topology Sperner's lemma. We also notice that our geometric ap-proach is strongly based on the as...

In this paper, we construct a special class of polynomials which converge uniformly to the solution of a non-local boundary value problem (NBVP). The use of this special class is justified by the physics of the model which is described by this NBVP. This NBVP has been studied by Palamides et al. (2009) in [2], where the existence of solutions is es...

In this paper we investigate the existence of multiple nontrivial solutions of a nonlinear heat flow problem with nonlocal boundary conditions. Our approach relies on the properties of a vector field on the phase plane and utilizes Sperner’s Lemma, combined with the continuum property of the solutions funnel.

An existence result for a singular third-order boundary value problem is proved in this work. Here the nonlinearity is of the form f(y)=(1−y)λg(y), where λ>0 and g(y) is continuous and positive on (0,1], and the boundary conditions are y(0)=0,y(+∞)=1,y′(+∞)=y″(+∞)=0. The problem arises in the study of draining and coating flows.

Existence results, by means of a simple approach, for the 3rd order differential equation x‴(t)=α(t)f(t,x(t),x′(t),x″(t)),0<t<1, satisfying the three-point boundary value conditions x(0)=x′(η)=x″(1)=0,x(0)=x′(η)=x″(1)=0, are given, where 0<η<10<η<1 is a fixed point in contrast to the usual case1/2<η<11/2<η<1, f(t,x,y,z)≥0f(t,x,y,z)≥0 for any t∈(0,1...

Consider the three-point boundary value problem for the 3$^{rd}$ order differential equation:
\begin{equation*}\left\{ \begin{aligned}
& x^{^{\prime \prime \prime }}(t)=\alpha \left( t\right) f(t,x(t),x^{\prime}\left( t\right) ,x^{\prime \prime }\left( t\right) ),\;\;\;0

In this article we investigate the existence of positive and/or negative solutions of a classes of four-point boundary-value problems for fourth-order ordinary differential equations. The assumptions in this article are more relaxed than the known assumptions. Our technique relies on the continuum property (connectedness and compactness) of the sol...

Existence results of positive solutions, by means of a new approaches, for the 3 the order three-point BVP x(t)=α(t)f(t,x(t),x(t),x(t)), x(0)=x(η)=x(1)=0, are given. Here 0<η<1 is a fixed point in contrast to the usual case 1/2<η<1. In addition, without any monotonicity assumption on the nonlinearity, we prove the existence of a sequence of such so...

This paper presents an upper and lower solution theory for singular boundary value problems modelling the Thomas–Fermi equation, subject to a boundary condition corresponding to the neutral atom with Bohr radius equal to its existence interval. Furthermore, we derive sufficient conditions for the existence–construction of the above-mentioned upper–...

If Y is a subset of the space ℝn × ℝn, we call a pair of continuous functions U, V Y-compatible, if they map the space ℝn into itself and satisfy Ux · Vy ≥ 0, for all (x, y) ∈ Y with x · y ≥ 0. (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary
differential n-dimensional system is inv...

The set Kc(F) of compact convex subsets of a Fréchet space F is studied in detail and is realized as a projective limit of metric spaces. The notion of Hausdorff metric on it is replaced by a family of corresponding “semi-metrics” which provide the necessary background for the support of continuity and Lipschitz continuity. Finally the notion of Hu...

Periodicity questions of differential systems on infinite-dimensional Hilbert spaces arestudied via a new methodology which is based on Fan-Knaster-Kuratowski-Mazurkiewicz theorem. We obtain in this way an alternative, to the classical fixed point theory, approach to the study of such type of problems with various applications on issues of mathemat...

In this paper we study singular boundary value problems on the half-line and we prove the existence of a global, monotone, positive and unbounded solution. The latter satisfies a Neumann condition at the origin and has prescribed asymptotic behavior at infinity. Our approach is based on a generalization of the Kneser's property (continuum) of the c...

In this article, we study a complete $n$-order differential equation subject to the $(p,n-p)$ right focal boundary conditions plus an additional nonlocal constrain. We establish sufficient conditions for the existence of a family of positive and monotone solutions at resonance. The emphasis in this paper is not only that the nonlinearity depends on...

In this paper, we study a type of non linear differential equations in Fréchet spaces. Some basic results, like existence and asymptotic behavior, are estab-lished. The approach proposed is based on the realization of differential equations in Fréchet spaces as projective limits of appropriate sequences of equations in Banach spaces. Mathematics Su...

In this paper we study the generalized logistic equation $$ frac{du}{dt}=a(t)u^{n}-b(t)u^{n+(2k+1)},quad n,kin mathbb{N}, $$ which governs the population growth of a self-limiting specie, with $a(t)$, $b(t)$ being continuous bounded functions. We obtain a unique global, positive and bounded solution which, further, plays the role of a frontier whic...

Consider the nonlinear scalar differential equation , where p and q are positive on (0, 1), “singular” at t = 0. 1 and/or y = 0 and fϵC(R+xR+xR+, R+), associated to the boundary conditions . We prove the existence of a global, positive and strictly increasing solution x = x(t) of this BVP, such that its “derivative” y = p(t)x(t) is also a positive...

Consider the nonlinear scalar differential equations 1/p(t)(p(t)y′(t))′ + sign(1 - α)q(t)f(t,y(t), p(t)y′(t)) = 0, where α > 0, α ≠ 1, p and q are "singular" at t=0, 1 and f ∈ C((0,1) × R+ × R-, R-), associated to boundary conditions γy(0) + δ lim t→ar0+ p(t)y′(t) = 0, γ > 0, limt→1- p(t)y′(t) = α limt→0+ p(t)y′(t). Existence of a monotone positive...

Consider the general nonlinear boundary-value problem (p(t)y'(t))' = p(t)q(t) f (t, y(t), y'(t)), t greater than or equal to 1, g(y(1), y'(1)) = 0, where the function f may be singular at the point y(1) = 0 and p(1) greater than or equal to 0. We obtain conditions which guarantee existence of positive and bounded solutions of the above problem. As...

We study the second-order ordinary differential equation $$ y''(t)=-f(t,y(t),y'(t)),quad 0leq tleq 1, $$ subject to the multi-point boundary conditions $$ alpha y(0)pm eta y'(0)=0,quad y(1)=sum_{i=1}^{m-2}alpha_iy(xi_i),. $$ We prove the existence of a positive solution (and monotone in some cases) under superlinear and/or sublinear growth rate in...

By utilizing a combination of properties of the consequent mapping with the Brouwer's fixed point theorem we obtain existence results for the nearly-periodic boundary value problem 2" = f (t , x , x ') , t â [O, 1 1 where Qo , Q 1 are complex valued nonsingular matrices. Let Cn denote the n-dimensional complex Euclidean linear space and let I be th...

Existence of a monotone positive solution with a prescribed slope of the singular boundary value problem 1 p(t)(p(t)y ' (t)) ' +sign(1-α)q(t)f(t,y(t),p(t)y ' (t))=0, γy(0)-δlim t→0+ p(t)y ' (t)=0,lim t→1- p(t)y ' (t)-αlim t→0+ p(t)y ' (t)=0 or γ x (1)+δlim t→1- p(t)x ' (t)=0,lim t→1- p(t)y ' (t)-αlim t→0+ p(t)y ' (t)· (0<α≠1, γ<0, δ≥0) is proved in...

Multipoint conjugate boundary value problems that arise in many technical applications are analyzed. The application of these problems in an eigenvalue problem is investigated. Solutions for the eigenvalue problem are discussed.

The existence of solutions of an abstract Nemytskii-type differential equation in a Hilbert space X satisfying a relationship of the form x(1) = G(x(0)) is investigated. Here G is a prespecified operator defined on X. c 2001 Academic Ress Key Words: operator equations in Hilbert spaces; boundary value problems.

In this paper, we investigate the existence of positive solutions of a second-order singular boundary value problem by constructing upper and lower solutions and combined them with properties of the consequent mapping.

Consider the higher-order nonlinear scalar differential equation where associated to the Lidstone boundary conditions Existence of a solution of boundary value problems (BVP) (1),(2) such that are given, under superlinear or sublinear growth in f. Similarly, existence for the BVP (1)–(3), under the same assumptions, is proved such that We further p...

Consider the higher-order nonlinear scalar differential equations x (2n) (t)=-f(t,x(t)),0≤t≤1(1) where f∈C([0,1]×[0,∞),(0,∞)), associated to the boundary conditions α i x (2i) (0)-β i x (2i+1) (0)=0γ i x (2i) (1)±δ i x (2i+1) (1)=0,(2) with α i ,γ i ,δ i ≥0, β i >0 (i=0,1,⋯,n-1). Existence of a solution of above boundary value problems (BVP s ) suc...

Sufficient conditions for the existence of a solution to the BVP x″ = f(t, x, x′), x(0) = Q0x(1), x′(0) = Q1x′(1) are obtained. Here Q0, Q1 are nonsingular n × n matrices, with Q0 orthogonal. These extend results for the periodic case and are proved via a modification of a degree-theoretic approach.

A new technique based on Kneser's theorem is introduced, to extend the topological method of Waewski for Caratheodory systems. In this line an existence theorem for a general boundary value problem is obtained as an application, as well as some asymptotic properties for semi-linear systems.

Consider the Ordinary Differential System {Mathematical expression} and a subset ω of Ω. It is known that the consequent mapping K is upper semicontinuous at any point P ∈ Ω at which K is defined and moreover K(P) is a continuum in ∂ω. Here we study the topological properties of the set K(P) in the case where P is a singular point of K, i.e. there...

## Projects

Project (1)