Existence of Periodic Solutions of a Class of Planar Systems

Abstract

In this paper, we consider the existence of periodic solutions for the following planar system:

where the function $H(u)\in C^3(\R^2\backslash \{0\},\,\R)$ is positive for $u\ne 0$ and positively $(q,\,p)$-quasi-homogeneous of quasi-degree $pq,\, \,G: \R^2\to \R^2$ is local Lipschitz and bounded, $h\in L^\infty(0,\,2\pi)$ is $2\pi$-periodic and $J$ is the standard symplectic matrix.