zbMATH — the first resource for mathematics

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.

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