Variational Approach to Quasi-Periodic Solution of Nonautonomous Second-Order Hamiltonian Systems

Abstract

We deal with the quasi-periodic solutions of the following second-order Hamiltonian systems $\ddot{x}$ $\left(t\right)=\nabla F\left(t,x\left(t\right)\right)$, where $x\left(t\right)=\left(x_1\left(t\right),\dots ,x_N\left(t\right)\right)$, and we present a new approach via variational methods and Minmax method to obtain the existence of quasi-periodic solutions to the above equation.