The critical hyperbola for a Hamiltonian elliptic system with weights

Abstract

In this paper we look for existence results for nontrivial solutions to the system, "equation is presented". with Dirichlet boundary conditions, u = v = 0 on ∂ Ω and α, β < N. We find the existence of a critical hyperbola in the (p,q) plane (depending on α, β and N) below which there exists nontrivial solutions. For the proof we use a variational argument (a linking theorem). © 2007 Springer-Verlag.