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New existence of periodic solutions for second order non-autonomous Hamiltonian systems. (English) Zbl 1201.37094
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 [{\it X. M. He} and {\it 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.

MSC:
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
34C25Periodic solutions of ODE
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References:
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