Boundedness and asymptotic behaviour of solutions of a nonlinear differential equation of the third order

Abstract

In this paper, we use Lyapunov second method. A complete Lyapunov function was constructed and used to obtain criteria for boundedness, uniform ultimate boundedness and asymptotic behaviour of solutions of a nonlinear differential equation of the third order. Our results revise, improve and extend existing results on boundedness, uniform ultimate boundedness and asymptotic behaviour of solutions of third order nonlinear differential equations in the literature.