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Existence and multiplicity of periodic solutions for a class of second-order Hamiltonian systems. (English) Zbl 1206.34059

By the use of variational methods, the authors prove the existence of nontrivial periodic solutions for some second order systems, assuming conditions on the nonlinearity both at zero and at infinity. They improve some known results for the case involving a potential with quadratic growth at infinity. In the case of a superquadratic and even potential, they use a symmetric mountain pass theorem to show that there are infinitely many periodic solutions.

MSC:

34C25 Periodic solutions to ordinary differential equations
47J30 Variational methods involving nonlinear operators
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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