Upper and lower solutions method for differential inclusions with integral boundary conditions
type: Item
instance of: scholarly article
title: Upper and lower solutions method for differential inclusions with integral boundary conditions
zbMATH Open document ID: 1122.34006
author: Mouffak Benchohra
author: Abdelghani Ouahab
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2007-03-19T00:00:00Z
review text: For a second-order differential inclusion, the authors consider a boundary value problem with nonlinear integral boundary conditions \[ y''(t)\in F(t, y(t)),\quad t\in [0,1], \] \[ y(0)- k_1 y'(0)= \int^1_0 h_1(y(s))\,ds, \] \[ y(1)+ k_2y'(1)= \int^1_0 h_2(y(s))\,ds. \] Here, \(F\) is a multivalued map with convex values that satisfies the Carathéodory conditions. The functions \(h_1\), \(h_2\) are continuous and nondecreasing, \(k_1\), \(k_2\) are nonnegative numbers. In terms of upper and lower functions, sufficient conditions are formulated for the existence of a solution. The proof is based on a nonlinear alternative of Leray-Schauder type.
reviewed by: Sergei A. Brykalov
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5134569
zbMATH Keywords: nonlinear integral boundary conditions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5134569