Nonlinear elliptic systems

Abstract

In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - Δu f(x, u, v, ∇u, ∇v), - Δ = g(x, u, v, ∇u, ∇v), in Ω, We discuss several classes of such systems using both variational and topological methods. The notion of criticality takes into consideration the coupling, which plays important roles in both a priori estimates for the solutions and Palais-Smale conditions for the associated functional in the variational case.