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Homoclinic and periodic orbits for Hamiltonian systems. (English) Zbl 0919.58026
Summary: This article deals with the existence of homoclinic and periodic solutions for second-order Hamiltonian systems. The main purpose is to consider unbounded potentials which do not satisfy the Ambrosetti-Rabinowitz condition. The method is variational and it combines a perturbation argument with Morse index estimates for minimax critical points.

MSC:
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
37G99 Local and nonlocal bifurcation theory for dynamical systems
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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References:
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