## 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

### Keywords:

periodic solution; Hamiltonian system; linking theorem
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