Ultimate Boundedness of Solutions for Certain Third Order Nonlinear Differential Equations

Abstract

We investigate in this paper, the ultimate boundedness of solutions for certain special class of third order nonlinear differential equations. Using suitable complete Lyapunov function, we obtain the criteria for the ultimate boundedness of solutions for this equation. Our result extends and improves on some well known results on boundedness of solutions of third order differential equations in the literature.

Key words: Nonlinear differential equations; Third order; Ultimate boundedness of solutions; Lyapunov’s method.