Some New Stability and Boundedness Results of Solutions of Lienard Type Equations With a Deviating Argument

Abstract

This paper concerns the stability and boundedness of solutions to the following Lienard type equation with a variable deviating argument, r(t): x ''(t) + f(1)(x(t), x(t - r(t)), x'(t), x'(t - r(t)))x'(t) + f(2)(x(t), x(t - r(t)), x'(t), x'(t - r(t)))(x'(t))(2) + g(1)(x(t)) + g(2)(x(t - r(t))) = p(t, x(t), x(t - r(t)), x'(t), x'(t - r(t))). By means of the Lyapunov second (direct) method, we obtain two new results on the subject and give an example for the illustration of the topic. (C) 2009 Elsevier Ltd. All rights reserved.