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Heteroclinic and homoclinic solutions for a singular Hamiltonian system. (English) Zbl 1160.37390

Summary: We consider an autonomous Hamiltonian system \(\ddot {q}+V_q(q)=0\) in \(\mathbb R^2\), where the potential \(V\) has a global maximum at the origin and singularities at some points \(\xi_1\), \(\xi_2 \in\mathbb R^2 \setminus \{0\}\). Under some compactness conditions on \(V\) at infinity and assuming a strong force type condition at the singularities, we study, using variational arguments, the existence of various types of heteroclinic and homoclinic solutions of the system.

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
34C25 Periodic solutions to ordinary differential equations
47J30 Variational methods involving nonlinear operators
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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