Nabla theorems and multiple solutions for some noncooperative elliptic systems

Abstract

We study some variational principles which imply the existence of multiple critical points for a functional $f$, using the properties of both $f$ and $\nabla f$ on some suitable sets. We derive some multiplicity theorems for a certain class of strongly indefinite functionals and we apply these results for finding multiple solutions of an elliptic system of reaction-diffusion type.