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Infinitely many homoclinic solutions for some second order Hamiltonian systems. (English) Zbl 1225.34051
Summary: We investigate the existence of infinitely many homoclinic solutions for a class of second order Hamiltonian systems. Using Zou’s fountain theorem we obtain two new criteria which guarantee that second order Hamiltonian systems have infinitely many homoclinic solutions. Recent results in the literature are generalized and significantly improved.

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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