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 $ lambda $, we consider the system $$displaylines{ -Delta v = lambda f(u) quad hbox{in } Omega , cr -Delta u = g(v) quad hbox{in } Omega , cr u = v=0 quad hbox{on } partial Omega , }$$ where $Omega$ is a smooth bounded domain in $mathbb{R}^N$ with $Ngeq 1$. One solution is obtained applying Ambrosetti and Rabinowitz's classical Mountain Pass Theorem, and the other solution by a local minimization. end{abstract}