Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 14, pp. 1-5.
Title: Boundedness of solutions for a Lienard
equation with multiple deviating arguments
Authors: Yuehua Yu (Hunan Univ. of Arts and Science, China)
Changhong Zhao (Hunan Univ. of Arts and Science, China)
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.