Existence and uniqueness of solution for a second order boundary value problem

Abstract

This paper deals with a second order boundary value problem with only integrals conditions. Our aim is to give new conditions on the nonlinear term; then, using Banach contraction principle and Leray Schauder nonlinear alternative, we establish the existence of nontrivial solution of the considered problem. As an application, some examples to illustrate our results are given.