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Zeitschrift für Analysis und ihre Anwendungen

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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