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.

Show me the PDF file (187 KB), TEX file, and other files for this article.

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

Return to the EJDE web page