## Periodic solutions of second order non-autonomous Hamiltonian systems with local superquadratic potential.(English)Zbl 1179.34037

The paper deals with the existence of T-periodic solutions for the second order Hamiltonian system
$-\ddot{u}(t)=\nabla_uF(t,\,u(t)),\quad a.\;e.\;\;t\in \mathbb{R}.$
In the case that $$F(t,u)$$ is locally superquadratic in $$u$$, the authors obtain some existence results for nontrivial T-periodic solutions. The discussion is based on a generalized mountain pass theorem.

### MSC:

 34C25 Periodic solutions to ordinary differential equations 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 58E30 Variational principles in infinite-dimensional spaces
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### References:

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