×

Nontrivial solutions for noncooperative elliptic systems at resonance. (English) Zbl 0963.35061

Summary: 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 condition.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J50 Variational methods for elliptic systems
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
PDFBibTeX XMLCite
Full Text: EuDML EMIS