On a superquadratic elliptic system with strongly indefinite structure

Abstract

In this paper, we consider the elliptic system \begin{equation*} \left\{\begin{array}{ll} -Δu=g(x,v)\,\, \textnormal{in}Ω, & \hbox{} -Δv=f(x,u)\,\,\textnormal{in}Ω, & \hbox{} u=v=0\textnormal{on}\partialΩ, & \hbox{} \end{array} \right. \end{equation*} where $\Omega$ is a bounded smooth domain in ${\mathbb{R}}^N$, and $f$ and $g$ satisfy a general superquadratic condition. By using variational methods, we prove the existence of infinitely many solutions. Our argument relies on the application of a generalized variant fountain theorem for strongly indefinite functionals. Previous results in the topic are improved.

12 pages

References in corpus (1)

• Periodic nonlinear Schrödinger equation with application to photonic crystals