Existence results for ϕ-Laplacian Dirichlet BVP of differential inclusions with application to control theory

In this paper, we study φ-Laplacian problems for differential inclusions with Dirichlet boundary conditions.We prove the existence of solutions under both convexity and nonconvexity conditions on the multivalued right-hand side.The nonlinearity satisfies either a Nagumotype growth condition or an integrably boundedness one.The proofs rely on the Bonhnenblust-Karlin fixed point theorem and the Bressan-Colombo selection theorem respectively.Two applications to a problem from control theory are provided.