Asymptotic behaviour of solutions of third order nonlinear differential equations

Abstract

In this paper, Lyapunov direct method was employed. We present criteria for all solutions x(t) its first and second derivatives of the third order nonlinear non autonomous differential equations to con- verge to zero as t → ∞. Sufficient conditions are also established for the boundedness and uniform ultimate boundedness of solutions of the equations considered. Our results revise, improve and generalize existing results in the literature.