Positive solutions for semipositone BVPs of second-order difference equations
type: Item
instance of: scholarly article
title: Positive solutions for semipositone BVPs of second-order difference equations
zbMATH Open document ID: 1148.39001
author: Dingyong Bai
author: Yuantong Xu
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2008-07-29T00:00:00Z
review text: The authors consider the following Sturm-Liouville discrete time problem \[ \triangle[p(t-1)\triangle u(t-1)] + \lambda f(t,u(t)) = 0 \;,\;a+1\leq t\leq b+1 \] \[ \gamma_1u(a) - \gamma_2p(a)\triangle u(a) = 0,\quad \gamma_3u(b+2)+\gamma_4p(b+1)\triangle u(b+1)=0 \] with \(\gamma_i\geq 0\), \(\gamma_1\gamma_3+\gamma_1\gamma_4+\gamma_2\gamma_3>0\), \(\lambda>0\) and \(\triangle\) the forward difference; also \(p(t)>0\), \(a\leq t\leq b+1\). Explicit conditions expressed through the properties of the nonlinearity \(f\) and the problem's coefficients are given, for the existence of at least one positive solution.
reviewed by: Vladimir Răsvan
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34L05
zbMATH DE Number: 5305213
zbMATH Keywords: difference equation
zbMATH Keywords: positive solution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5305213