Existence results for quasilinear elliptic equations with multivalued nonlinear terms

In this paper we study the existence of solutions (Formuala presented) with Apu G (Formuala presented) for the Dirichlet problem where (Formuala presented) is a bounded open set with boundary (Formuala presented) stands for the p—Laplace differential operator, (Formuala presented) denotes the subdifferential (in the sense of convex analysis) of a proper convex and lower semicontinuous function (Formuala presented) and (Formuala presented) is a multivalued map. We prove two existence results: the first one deals with the case where the multivalued map (Formuala presented) is upper semicontinuous with closed convex values and the second one deals with the case when (Formuala presented) is lower semicontinuous with closed (not necessarily convex) values.