On the Asymptotic Behavior of Solutions of Certain Second-Order Differential Equations

Abstract

In this paper, the second order non-linear differential equation (x) over dot + a(t)f (x, (x) overdot)(x) over dot+ b(t)g(x) = p(t, x, (x) over dot) is considered, and Lyapunov's second method is used to show that uniform boundedness and convergence to zero of all solutions of this equation together with their derivatives of the first order. (c) 2006 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.