Ou, Zeng-Qi; Tang, Chun-Lei Existence and multiplicity results for some elliptic systems at resonance. (English) Zbl 1172.35382 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7-8, 2660-2666 (2009). Summary: The existence and multiplicity of weak solutions for some resonant elliptic systems are obtained by using Ekeland’s variational principle, the mountain pass theorem and the saddle point theorem in critical point theory. Cited in 18 Documents MSC: 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 35J50 Variational methods for elliptic systems 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 35D05 Existence of generalized solutions of PDE (MSC2000) Keywords:resonance; elliptic systems; Ekeland’s variational principle; mountain pass theorem; saddle point theorem PDFBibTeX XMLCite \textit{Z.-Q. Ou} and \textit{C.-L. Tang}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 7--8, 2660--2666 (2009; Zbl 1172.35382) Full Text: DOI References: [1] Mawhin, J.; Schmitt, K., Nonlinear eigenvalue problems with the parameter near resonance, Ann. Polon. Math., 51, 241-248 (1990) · Zbl 0724.34025 [2] Ma, T. F.; Ramost, M.; Sanchez, L., Multiple solutions for a class of nonlinear boundary value problem near resonance: A variational approach, Nonlinear Anal. TMA, 30, 3301-3311 (1997) · Zbl 0887.35053 [3] Ma, T. F.; Pelicer, M. L., Perturbations near resonance for the \(p\)-Laplacian in \(R^N\), Abstr. Appl. Anal., 7, 323-334 (2002) · Zbl 1065.35116 [4] Chang, K. C., Principal eigenvalue for weight in elliptic systems, Nonlinear Anal., 46, 419-433 (2001) · Zbl 1194.35135 [5] Furtado, M. F.; de Paiva, F. O.V., Multiplicity of solutions for resonant elliptic systems, J. Math. Anal. Appl., 319, 435-449 (2006) · Zbl 1108.35046 [6] Costa, D. G., On a class of elliptic systems in \(R^N\), Electron J. Differential Equations, 7, 1-14 (1994) [7] Furtado, M. F.; Maia, L. A.; Silva, E. A.B., Solutions for a resonant elliptic system with coupling in \(R^N\), Comm. Partial Differential Equations, 27, 1515-1536 (2002) · Zbl 1016.35022 [8] Li, G.; Yang, J., Asymptotically linear elliptic systems, Comm. Partial Differential Equations, 29, 925-954 (2004) · Zbl 1140.35406 [9] Zou, W. M., Multiple solutions for asymptotically linear elliptic systems, J. Math. Anal. Appl., 255, 213-229 (2001) · Zbl 0989.35049 [10] Costa, D. G.; Magalhaes, C. A., A variational approach to subquadratic perturbations of elliptic systems, J. Differential Equations, 111, 103-122 (1994) · Zbl 0803.35052 [11] Costa, D. G.; Magalhaes, C. A., Existence results for perturbations of the \(p\)-Laplacian, Nonlinear Anal., 24, 409-418 (1995) · Zbl 0818.35029 [12] Bartolo, P.; Benci, V.; Fortunato, D., Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Anal., 7, 981-1012 (1983) · Zbl 0522.58012 [13] Rabinowitz, P. H., Minimax methods in critical point theory with applications to differential equations, (CBMS. Reg. Conf. Ser. in Math., vol. 65 (1986), Amer. Math. Soc.: Amer. Math. Soc. Providence, RI), 1-100 · Zbl 0609.58002 [14] Silva, E. A.B., Subharmonic solutions for subquadratic Hamiltonian systems, J. Differential Equations, 115, 120-145 (1995) · Zbl 0814.34025 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.