Existence of solution, Filippov's Theorem and compactness of the set of solutions for a third-order differential inclusion with three- point boundary conditions

Abstract

In this paper, we study a third-order differential inclusion with three-point boundary conditions. We prove the existence of a solution under convexity conditions on the multi-valued right-hand side; the proof is based on a nonlinear alternative of Leray-Schauder type. We also study the compactness of the set of solutions and establish some Filippov's- type results for this problem.