Subharmonic and multiple subharmonic solutions for second order differential systems

Abstract

We show existence and multiple existence results of subharmonic solutions for the system of second order differential equation $\ddot{u}(t)+ G'(u(t))=f(t)$ for $t\in \mathbb R$, where $N \in \mathbb N$, $f \in C(\mathbb R, \mathbb R^N)$ is a $T$-periodic function, $G\in C^{2}(\mathbb R^{N},\mathbb R)$ is a nonconvex functional.