Uniform boundedness of solutions for a class of Lienard equations

Abstract

In this article, we study a class of Lienard equations $$ x''(t)+f(x(t))x'(t)+g_1(x(t))+g_2(x(t-au(t))=e(t). $$ 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.

Keywords

• Second order differential equations
• cosine function of operators
• abstract Cauchy problem