Strongly nonlinear second order multivalued Dirichlet systems

Abstract

We consider second order nonlinear Dirichlet systems driven by a nonlinear nonhomogeneous differential operator. The reaction term consists of a maximal monotone map A(⋅) plus a multivalued perturbation F depending also on derivative. Using tools from multivalued analysis and from the theory of nonlinear operators of monotone type, we prove existence theorems both for the "convex" (F is convex-valued) and the "nonconvex" (F is nonconvex-valued) problems. We also present an example of a system with unilateral constraint.