Electron. J. Diff. Eqns., Vol. 2009(2009), No. 97, pp. 1-5.

Uniform boundedness of solutions for a class of Lienard equations

Guo-Rong Ye, Hui-Sheng Ding, Xi-Lang Wu

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.

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Guo-Rong Ye
College of Mathematics and Information Science
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: yeguorong2006@sina.com
Hui-Sheng Ding
College of Mathematics and Information Science
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: dinghs@mail.ustc.edu.cn
Xi-Lang Wu
College of Mathematics and Information Science
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: wuxilang99@sina.com

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