Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 97, pp. 1-5.
Title: Uniform boundedness of solutions for a class of
Lienard equations
Authors: Guo-Rong Ye (Jiangxi Normal Univ. Nanchang, China)
Hui-Sheng Ding (Jiangxi Normal Univ. Nanchang, China)
Xi-Lang Wu (Jiangxi Normal Univ. Nanchang, China)
Abstract:
In this article, we study a class of Lienard equations
$$
x''(t)+f(x(t))x'(t)+g_1(x(t))+g_2(x(t-\tau(t))=e(t).
$$
Under some suitable conditions, we ensure that all solutions
of the above Lienard equations are uniformly bounded.
Our assumptions are less restrictive than those in [9];
thus we extend some previous results.
Submitted December 2, 2008. Published August 11, 2009.
Math Subject Classifications: 35R10, 47D09.
Key Words: Second order differential equations;
cosine function of operators; abstract Cauchy problem.