Silva, Elves A. B. Nontrivial solutions for noncooperative elliptic systems at resonance. (English) Zbl 0963.35061 Electron. J. Differ. Equ. 2001, Conf. 06, 267-283 (2001). 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. Cited in 9 Documents 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 Keywords:variational methods; resonant problem; strongly indefinite functionals PDFBibTeX XMLCite \textit{E. A. B. Silva}, Electron. J. Differ. Equ. 2001, 267--283 (2001; Zbl 0963.35061) Full Text: EuDML EMIS