On the Stability and Boundedness of Solutions of Nonlinear Third Order Differential Equations With Delay

Abstract

By defining a Lyapunov functional, we investigate the stability and boundedness of solutions to nonlinear third order differential equation with constant delay, r; x'''(t) + g(x(t)) x''(t) + f(x(t-r), x'(t-r)) + h(x(t-r)) = p(t, x(t), x' (t), x(t-r), x''(t)), when p(t, x(t), x'(t), x(t-r), x'(t-r), x''(t)) =0 and not equal 0, respectively. Our results achieve a stability result which exists in the relevant literature of ordinary nonlinear third order differential equation without delay to the above functional differential equation for the stability and boundednes of solutions. An example is introduced to illustrate the importance of the results obtained.