Abstract

We establish the existence of weak solutions in an Orlicz-Sobolev space to the Dirichlet problem (D) {(-div (a(-del u(x)-)del u(x)))(u = 0), (= g(x, u),) (in Omega)(on partial derivative Omega,) where Omega is a bounded domain in R-N, g is an element of C(<(Omega)over bar> x R, R), and the function phi(s) = sa(-s-) is an increasing homeomorphism from R onto R. Under appropriate conditions on phi, g, and the Orlicz-Sobolev conjugate Phi(*) of Phi(s) = integral(0)(s) phi(t) dt, (conditions which reduce to subcriticality and superlinearity conditions in the case the functions are given by powers), we obtain the existence of nontrivial solutions which are of mountain pass type.