Existence of solutions for a class of boundary value problems of semilinear differential inclusions
In this paper, a class of boundary problems for second order semilinear differential inclusions is studied. By applying techniques from multivalued analysis and fixed point theorems due to Covitz-Nadler, Bohnenblust-Karlin and Schaefer, some existence results of solutions are presented for the nonlinear term which is a Lipschitz continuous, upper or lower semicontinuous multivalued map, respectively. As consequences some existence conditions of solutions are given for a class of second order semilinear differential systems. (C) 2012 Elsevier Ltd. All rights reserved.
existence of solutions boundary value problem differential inclusion fixed point