Existence and multiplicity of periodic solutions for a class of dynamical systems

Abstract

In this paper, we study the existence and multiplicity of periodic
solutions of the dynamical system class
\begin{equation*}
\ddot{u}(t)+A\dot{u}(t)+V'(t,u(t))=0,
\end{equation*}
where A is a skew-symmetric constant matrix, t $\in\mathbb{R}$,
$u\in\mathbb{R}^N$ and V $\in
C^1(\mathbb{R}\times\mathbb{R}^N,\mathbb{R})$ is T-periodic in t, with $T>0$. By using the minimax methods in critical point theory, we prove some existence results which generalize and improve some existing results in the literature.