The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (141 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
Volume 25, Issue 2, 2006, pp. 237–248
DOI: 10.4171/ZAA/1286

Published online: 2006-06-30

Existence of Periodic Solutions of a Class of Planar Systems

Xiaojing Yang[1]

(1) Tsinghua University, Beijing, China

In this paper, we consider the existence of periodic solutions for the following planar system: $$ J u'=\D H(u)+ G(u)+h(t)\,, $$ 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.

Keywords: Periodic solutions, resonance, planar systems

Yang Xiaojing: Existence of Periodic Solutions of a Class of Planar Systems. Z. Anal. Anwend. 25 (2006), 237-248. doi: 10.4171/ZAA/1286