A multiplicity result for a class of superquadratic Hamiltonian systems

Abstract

We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter λ, we consider the system -∆v = λƒ(u) in Ω, -∆u = g(v) in Ω, u = v = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝN with N ≥ 1. One solution is obtained applying Ambrosetti and Rabinowitz's classical Mountain Pass Theorem, and the other solution by a local minimization.