Boundedness of solutions to a retarded Liénard equation

Wei Long, Jiangxi Normal University, Nanchang, Jiangxi, P. R. China
Hong-Xia Zhang, Jiangxi Normal University, Nanchang, Jiangxi, P. R. China

E. J. Qualitative Theory of Diff. Equ., No. 24. (2010), pp. 1-9.

Abstract: This paper is concerned with the following retarded Li\'{e}nard equation

$$x''(t)+f_1(x(t))(x'(t))^2+f_2(x(t))x'(t)+g_1(x(t))+g_2(x(t-\tau(t)))=e(t).$$

We prove a new theorem which ensures that all solutions of the above Li\'{e}nard equation satisfying given initial conditions are bounded. As one will see, our results improve some earlier results even in the case of $f_1(x)\equiv 0$.

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