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Infinitely many homoclinic orbits for the second-order Hamiltonian systems. (English) Zbl 1039.37044
Summary: The existence of homoclinic orbits for the second-order Hamiltonian systems without periodicity is studied and infinitely many homoclinic orbits for both superlinear and asymptotically linear cases are obtained.

MSC:
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37C29 Homoclinic and heteroclinic orbits for dynamical systems
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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