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

Fei, Guihua

Electron. J. Differ. Equ. 2002, Paper No. 08, 12 p. (2002).

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