Stability criteria for certain third order nonlinear delay differential equations

Abstract

In this paper we study the asymptotic stability of the trivial solution of third order nonlinear delay differential equations of the form

x'''(t) + f(x(t), x'(t))x''(t) + g(x(t − r), x'(t − r)) + h(x(t − r)) = 0,

where r > 0 is a constant delay. In proving our result we make use of Lyapunov’s second method by constructing a Lyapunov functional.