JournalszaaVol. 25 , No. 2DOI 10.4171/zaa/1286

Existence of Periodic Solutions of a Class of Planar Systems

  • Xiaojing Yang

    Tsinghua University, Beijing, China
Existence of Periodic Solutions of a Class of Planar Systems cover

Abstract

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

Ju=\DH(u)+G(u)+h(t),J u'=\D H(u)+ G(u)+h(t)\,,

where the function H(u)C3(R2\{0},R)H(u)\in C^3(\R^2\backslash \{0\},\,\R) is positive for u0u\ne 0 and positively (q,p)(q,\,p)-quasi-homogeneous of quasi-degree pq,G:R2R2pq,\, \,G: \R^2\to \R^2 is local Lipschitz and bounded, hL(0,2π)h\in L^\infty(0,\,2\pi) is 2π2\pi-periodic and JJ is the standard symplectic matrix.