## Infinitely many periodic solutions for subquadratic second-order Hamiltonian systems.(English)Zbl 1294.34047

Summary: Consider the second-order Hamiltonian systems \begin{aligned} & \ddot u(t)+\nabla_uW(t,u)=0\quad\forall t\in\mathbb R,\\ & u(0)=u(T),\quad \dot u(0)=\dot u(T),\quad T>0,\end{aligned} where $$W(t,u)$$ is $$T$$-periodic in $$t$$. We investigate the existence of infinitely many periodic solutions for a class of subquadratic nonautonomous second-order Hamiltonian systems by using the variant fountain theorem.

### MSC:

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

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