Existence of weak solutions for a boundary value problem of a second order ordinary differential equation

Abstract

The aim of this paper is to investigate the existence of weak solutions for a boundary value problem of a second order differential equation. As the main tool, we apply a Krasnosel'skii type fixed point theorem in conjunction with the technique of measures of weak noncompactness in Banach spaces. Finally, two examples are given to illustrate our abstract results. MSC: 35G30; 47H08; 47H09