Abstract

We establish the existence of weak solutions to the inclusion problem {?u(x) ? ?(|v(x)|) sgn v(x), x in ? -div v (x) = g(x, u(x)), x in ?, u = 0 on ?? where ? is a bounded domain in ?N, g ? C (?? × ?, ?), and ? ? ? × ? is a maximal monotone odd graph. Under suitable conditions on ?, g (which reduce to subcritical and superlinear conditions in the ease of powers) we obtain the existence of non-trivial solutions which are of mountain pass type in an appropriate not necessarily reflexive Orlicz Sobolev space. The proof is based on a version of the Mountain Pass Theorem for a non-smooth case.