Uniform stability, boundedness and asymptotic behaviour of solutions of some third order nonlinear delay differential equations.

Abstract

In this paper, sufficient conditions are established for uniform asymptotic stability of the trivial solutions, uniform boundedness, uniform ultimate boundedness and asymptotic behaviour of solutions of some third order nonlinear neutral delay differential equations. We employ Lyapunov’s direct method by constructing a complete Lyapunov functional to obtain the results. Recent results on third order nonlinear delay differential equations are particular cases of our results.