Lv, Ying; Tang, Chun-Lei Existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems with superquadratic potential. (English) Zbl 1267.34074 Abstr. Appl. Anal. 2013, Article ID 328630, 12 p. (2013). Authors’ abstract: In this paper the authors investigate the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems \(\ddot{u}(t)-L(t)u(t)+\nabla W(t,u(t))=0\) where \(L\in C(\mathbb{R},\mathbb{R}^{N^{2}})\) is a symmetric matrix-valued function and \(W\in C^{1}(\mathbb{R}\times\mathbb{R}^{N},\mathbb{R})\) satisfies some local superquadratic conditions without the so-called Ambrosetti-Rabinowitz condition and any periodicity assumptions on both \(L\) and \(W\). For the proof, they apply the ““mountain pass theorem” and the “fountain Theorem” to the least action integral. Reviewer: Mohsen Timoumi (Monastir) Cited in 4 Documents MSC: 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 58E50 Applications of variational problems in infinite-dimensional spaces to the sciences Keywords:homoclinic orbits; Hamiltonian systems; superquadratic potential; Minimax methods × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Poincaré, H., Les Méthods Nouvelles de la Mécanique Céleste (1897-1899), Paris, France: Gauthier-Villars, Paris, France [2] Coti Zelati, V.; Ekeland, I.; Séré, E., A variational approach to homoclinic orbits in Hamiltonian systems, Mathematische Annalen, 288, 1, 133-160 (1990) · Zbl 0731.34050 · doi:10.1007/BF01444526 [3] Felmer, P. L.; de Barros e. Silva, E. 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