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Homoclinic orbits for a class of symmetric Hamiltonian systems. (English) Zbl 0788.34042
Summary: We study existence of homoclinic orbits for a class of Hamiltonian systems that are symmetric with respect to independent variable (time). For the scalar case we prove existence and uniqueness of a positive homoclinic solution. For the system case we prove existence of symmetric homoclinic orbits. We use variational approach.

MSC:
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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