Upper and lower solutions method for differential inclusions with integral boundary conditions

Mouffak Benchohra,Abdelghani Ouahab

doi:10.1155/jamsa/2006/10490

Abstract

A nonlinear alternative of the Leray-Schauder type for multivalued maps combined with upper and lower solutions is used to investigate the existence of solutions for second-order differential inclusions with integral boundary conditions.

Highlights

This paper is concerned with the existence of solutions for the second-order boundary value problem:y (t) ∈ F t, y(t), a.e. t ∈ J := [0, 1], y(0) − k1 y (0) = h1 y(s) ds,0 1 y(1) + k2 y (1) = h2 y(s) ds, where F : J × R → ᏼ(R) is a compact convex-valued multivalued map, ᏼ(R) is the family of all nonempty subsets of R, hi : R → R (i = 1, 2) are continuous functions, and ki are nonnegative constants.Boundary value problems with integral boundary conditions constitute a very interesting and important class of problems
For boundary value problems with integral boundary conditions and comments on their importance, we refer the reader to the papers [9, 14, 19] and the references therein
Boundary value problems with integral boundary conditions have been studied by a number of authors, for example, [4, 6, 16]

Summary

Introduction

This paper is concerned with the existence of solutions for the second-order boundary value problem:. Boundary value problems with integral boundary conditions constitute a very interesting and important class of problems. For boundary value problems with integral boundary conditions and comments on their importance, we refer the reader to the papers [9, 14, 19] and the references therein. Boundary value problems with integral boundary conditions have been studied by a number of authors, for example, [4, 6, 16].

Preliminaries

Main result