## 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 [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.

### MSC:

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

Zbl 1133.37025
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### References:

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