Discrete conjugate boundary value problems
type: Item
instance of: scholarly article
title: Discrete conjugate boundary value problems
zbMATH Open document ID: 0976.39001
DOI: 10.1016/S0893-9659(99)00171-8
author: Ravi P. Agarwal
author: Donal O'Regan
published in: Applied Mathematics Letters
publication date: 2002-01-02T00:00:00Z
review text: Consider the discrete boundary value problem \[ \begin{aligned} & (-1)^{n-p}\Delta^n y(i-p)=f(i,y(i)),\quad i\in J_p,\\ & y(0)= \dots y(p-1)=0,\\ & y(T+p+1)=\dots=y(T+n)=0,\end{aligned} \] where \(T\in\{1,2,\dots\}\), \(J_p=\{p,p+1,\dots,T+p\}\), \(1\leq p\leq n-1\), \(n\geq 2\) and \(y:I_n=\{0,1,\dots,T+n\}\to\mathbb{R}\). If \(f:J_p\times [0,\infty)\to [0,\infty)\) is a continuous, nondecreasing function, if there exists a continuous, nondecreasing function \(\psi:[0,\infty)\to [0,\infty)\) such that \(\psi>0\) on \((0,\infty)\) and a function \(g:J_p\to[0,\infty)\) such that \[ f(k,u)\leq g(k)\psi(u) \text{ for all }u>0\text{ and }k\in J_p, \] and if \(\sup_{c\in (0,\infty)}(c/\psi(c))>Q\), where \(Q\) denotes certain constants, then the problem under consideration has a nonnegative solution. An analogous result is obtained for singular problems.
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 1428512
zbMATH Keywords: conjugate boundary value problems
zbMATH Keywords: both singular and nonsingular type
zbMATH Keywords: discrete boundary value problem
zbMATH Keywords: nonnegative solution
reviewed by: Dobiesław Bobrowski
MaRDI profile type: Publication
cites work: On the existence of positive solutions of higher order difference equations
cites work: Eigenvalues and eigenfunctions of discrete conjugate boundary value problems
cites work: Q4230136
cites work: Q4337944
cites work: Extension of continuous and discrete inequalities due to Eloe and Henderson
cites work: Singular discrete boundary value problems
cites work: A fixed-point approach for nonlinear discrete boundary value problems
cites work: Q4033029
cites work: A generalization of concavity for finite differences
cites work: A discrete boundary value problem
full work available at URL: s0893-9659(99)00171-8
OpenAlex ID: W2048460265
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description: scientific article; zbMATH DE number 1428512