ON SUPERQUADRATIC ELLIPTIC-SYSTEMS

In this article we study the existence of solutions for the elliptic system -DELTAu = partial derivative H/partial derivative v (u, v, x) in OMEGA, -DELTAv = partial derivative H/partial derivative u (u, v, x) in OMEGA, u = 0, v = 0 on partial derivative OMEGA. where OMEGA is a bounded open subset of R(N) with smooth boundary partial derivative OMEGA, and the function H : R2 x OMEGABAR --> R, is of class C1 . We assume the function H has a superquadratic behavior that includes a Hamiltonian of the form H(u, v) = \u\alpha + \v\beta where 1 - 2/N 1, beta > 1. We obtain existence of nontrivial solutions using a variational approach through a version of the Generalized Mountain Pass Theorem. Existence of positive solutions is also discussed.34319911