Periodic solutions for a class of nonautonomous second order Hamiltonian systems. (English) Zbl 1133.37025

He, Xiumei; Wu, Xian

J. Math. Anal. Appl. 341, No. 2, 1354-1364 (2008).

Summary: In this paper, some existence theorems of periodic solutions of a class of the nonautonomous second order Hamiltonian systems
\[ \ddot x(t)-B(t)x(t)+\nabla H(t,x(t))=0,\quad t\in [0,T], \]
are obtained by a mountain pass theorem and a local link theorem.

MSC:

37J45	Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
34C25	Periodic solutions to ordinary differential equations

Keywords:

Hamiltonian systems; periodic solutions; mountain pass theorem; local link

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