Strongly nonlinear multivalued boundary value problems Original Research Article

In this paper we study nonlinear second-order differential inclusions involving the differential operator depending on both: unknown function x and its derivative x′, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and can be applied to the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, we obtain solutions for both the “convex” and “nonconvex” problems. Finally, we present the cases of special interest, which fit into our framework, illustrating the generality of our results.