On the existence of positive solutions of fourth-order difference equations
type: Item
instance of: scholarly article
title: On the existence of positive solutions of fourth-order difference equations
zbMATH Open document ID: 1068.39008
author: Zhimin He
author: Jianshe Yu
published in: Applied Mathematics and Computation
publication date: 2005-02-22T00:00:00Z
review text: Let \(T\geq 1\) fixed, \(f\in C(\mathbb{R}^+,\mathbb{R}^+)\), \(a:\{1,2,\dots, T+1\}\subset\mathbb{Z}\to \mathbb{R}^+\) and \(\lim_{x\to 0,x> 0}\,x^{-1} f(x)\) and \(\lim_{x\to+\infty}\, x^{-1} f(x)\) be limits that exist. The authors determine eigenvalues \(\lambda\) for which there exist positive solutions \(u\) of the fourth-order difference equation \[ \Delta^4 u(t- 2)- \lambda a(t) f(u(t))= 0,\quad t\in \{2,3,\dots, T+ 2\}\subset\mathbb{Z} \] satisfying the boundary conditions \[ u(0)= \Delta^2 u(0)= u(T+ 2)= \Delta^2 u(T)= 0 \] or \[ u(0)= \Delta^2 u(0)= \Delta u(t+ 1)= \Delta^3 u(T- 1)= 0 \] by means of Krasnosel'skij's fixed point theorem.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 2136133
zbMATH Keywords: Positive solution
zbMATH Keywords: Krasnosel'skii's fixed point theorem
zbMATH Keywords: boundary value problem
zbMATH Keywords: fourth-order difference equation
reviewed by: Dan-Mircea Borş
MaRDI profile type: Publication
full work available at URL: j.amc.2003.12.016
OpenAlex ID: W2084898026
cites work: Positive solutions and nonlinear eigenvalue problems for third-order difference equations
cites work: Q4351782
cites work: Two positive solutions of a boundary value problem for difference equations
cites work: A fixed-point approach for nonlinear discrete boundary value problems
cites work: Positive solutions for nonlinear eigenvalue problems
cites work: Existence of positive solutions for BVPs of fourth-order difference equations
cites work: On the existence of positive solutions of fourth-order ordinary differential equations
cites work: On a nonlinear boundary value problem for fourth order equations
cites work: Q5732050
cites work: Q5185568
DOI: 10.1016/J.AMC.2003.12.016
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description: scientific article; zbMATH DE number 2136133