Electron. J. Diff. Eqns., Vol. 2009(2009), No. 14, pp. 1-5.

Boundedness of solutions for a Lienard equation with multiple deviating arguments

Yuehua Yu, Changhong Zhao

Abstract:
We consider the Lienard equation
$$ x''(t)+f_1 (x(t)) (x'(t))^{2}+f_2 (x(t)) x'(t)+g_0(x(t)) +\sum_{j=1}^{m} g_{j}(x(t-\tau_{j}(t)))=p(t), $$
where $f_1$, $f_2$, $g_1 $ and $g_2$ are continuous functions, the delays $\tau_j(t)\geq 0$ are bounded continuous, and $p(t)$ is a bounded continuous function. We obtain sufficient conditions for all solutions and their derivatives to be bounded.

Submitted December 15, 2008. Published January 13, 2009.
Math Subject Classifications: 34C25, 34K13, 34K25.
Key Words: Lienard equation; deviating argument; bounded solution.

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Yuehua Yu
Department of Mathematics
Hunan University of Arts and Science
Changde, Hunan 415000, China
email: jinli127@yahoo.com.cn
Changhong Zhao
Department of Mathematics
Hunan University of Arts and Science
Changde, Hunan 415000, China
email: hongchangzhao@yahoo.com.cn

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