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On periodic solutions of superquadratic Hamiltonian systems. (English) Zbl 0999.37039

Summary: The author studies the existence of periodic solutions for some Hamiltonian systems \(\dot z=JH_{z}(t,z)\) under new superquadratic conditions which cover the case \(H(t,z)=|z|^{2}(\ln (1+|z|^{p}))^q \) with \(p, q>1\). By using the linking theorem, we obtain some new results.

MSC:

37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34C25 Periodic solutions to ordinary differential equations
37B30 Index theory for dynamical systems, Morse-Conley indices
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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