Existence Theorems for Nonlinear Boundary Value Problems for Second Order Differential Inclusions

In this paper we consider a nonlinear two-point boundary value problem for second order differential inclusions. Using the Leray–Schauder principle and its multivalued analog due to Dugundji–Granas, we prove existence theorems for convex and nonconvex problems. Our results are quite general and incorporate as special cases several classes of problems which are of interest in the literature