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Qualitative Analysis for a Class of Second-order Nonlinear System with Delay

Authors:

Qi-lin Peng

Affiliation:

Department of Basic Science, Suqian Vocational and Technological College, Suqian, Jiangsu 223800

Abstract:

The second-order nonlinear system with delay

$$x'(t) + f(x(t),x'(t)) + g(x(t),x'(t))psi (x(t - tau )) = p(t)$$

being considered. Four theorems on the stability of zero solution, the boundedness of the solutions, the existence of the periodic solutions, the existence and uniqueness of the stationary oscillation are obtained by means of the Liapunov's second method. The conclusion in the literatures are generalized.

Keywords:

second_order nonlinear differential equation delay Liapunov functional

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