On Asymptotic Stability of Solutions To Third Order Nonlinear Differential Equations With Retarded Argument

Abstract

In this paper, we are concerned with the asymptotic stability of the trivial solution of third order nonlinear delay differential equations of the form x″(t) + φ(x(t), x′(t))x″(t) + φ(x(t - r(t)), x′(t - r(t)) + h(x(t - r(t))) = 0. By constructing a Lyapunov functional, we establish some new sufficient conditions which insure that the trivial solution of this equation is the asymptotically stable. In particular, an example is given to illustrate the importance of our result. © Dynamic Publishers, Inc.