GENERALIZED SCHRODINGER-POISSON TYPE SYSTEMS

In this paper we study the boundary value problem {-Delta u + epsilon q Phi f(u) = eta vertical bar u vertical bar p(-1)u in Omega, -Delta Phi = 2qF(u) in Omega, u = Phi = 0 on partial derivative Omega, where Omega C R-3 is a smooth bounded domain, 1 < p < 5, epsilon, n = +/- 1, q > 0, f : R -> R is a continuous function and F is the primitive of f such that F(0) = 0. We provide existence and multiplicity results assuming on f a sub-critical growth condition. The critical case is also considered and existence and nonexistence results are proved.