## A periodic solution for a second-order asymptotically linear Hamiltonian system.(English)Zbl 1167.34345

Summary: We study the existence of a periodic solution of the following second-order Hamiltonian system:
$\ddot u (t)+\nabla F(t,u(t))=0,\qquad t\in [0,T],$
where $$F(t,x)= - K(t,x)+W(t,x)$$. Assuming that $$K$$ satisfies the “pinching” condition and $$W$$ is asymptotically linear at infinity, the existence of a nontrivial periodic solution is obtained via the Mountain Pass Theorem.

### MSC:

 34C25 Periodic solutions to ordinary differential equations 47J30 Variational methods involving nonlinear operators 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
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### References:

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