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.


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