Strongly nonlinear second order multivalued Dirichlet systems

© 2018 Journal of Nonlinear and Variational Analysis 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 the 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 convex-valued) and the”nonconvex” (F nonconvex-valued) problems. We also present an example of a system with unilateral constraints