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Some critical point theorems and their applications to periodic solution for second order Hamiltonian systems. (English) Zbl 1191.34053
Some critical point theorems with lack of compactness are deduced by means of the reduction method, the perturbation argument and the least action principle. These abstract results are applied under relaxed assumptions, and the main application is devoted to the existence of periodic solutions for nonautonomous second order Hamiltonian systems.

MSC:
34C25 Periodic solutions to ordinary differential equations
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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