New existence of periodic solutions for second order non-autonomous Hamiltonian systems. (English) Zbl 1201.37094

Zhang, Qiongfen; Tang, X. H.

J. Math. Anal. Appl. 369, No. 1, 357-367 (2010).

The authors consider the second order Hamiltonian system \(\ddot x(t)-B(t)x(t)+\nabla H(t,x)=0\). They show that under some conditions on \(B\) and \(H\) this system has a nontrivial periodic solution. The results extend those contained in [X. M. He and X. Wu, J. Math. Anal. Appl. 341, No. 2, 1354–1364 (2008; Zbl 1133.37025)]. The proofs use a linking and a local linking argument for the Euler-Lagrange functional corresponding to the problem.

Reviewer: Andrzej Szulkin (Stockholm)

MSC:

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

Keywords:

periodic solution; linking theorem; local linking theorem; second order Hamiltonian system

Citations:

Zbl 1133.37025

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