On The Stability, Boundedness And Square Integrability Of A Class Of Third Order Neutral Differential Equations

Abstract

A non-linear neutral delay differential equation of the third order is considered. Using Lyapunov’s direct method, we have derived new sufficient conditions for the uniform asymptotic stability of the zero solution as well as the boundedness and square integrability of all solutions. The results here will be of interest to other researchers working on qualitative behavior of solutions of differential equations.