Nontrivial solutions for noncooperative elliptic systems at resonance

Abstract

In this article we establish the existence of a nonzero solution for variational noncooperative elliptic systems under Dirichlet boundary conditions and a resonant condition at infinity. Situations where the problem is nonresonant and resonant at the origin are considered. The results are based on a version of a critical point theorem for strongly indefinite functionals which are asymptotically quadratic at infinity and do not satisfy any Palais-Smale type condition.

Keywords

• Noncooperative systems
• variational methods
• resonant problem.