No abstract

Stability, boundedness and existence of a unique periodic solution to certain second order nonlinear delay differential equations is discussed. By employing Lyapunov's direct (or second) method, a complete Lyapunov functional is constructed and used to establish sufficient conditions, on the nonlinear terms, that guarantee uniform asymptotic stability, uniform ultimate boundedness and existence of a unique periodic solution. Obtained results complement many outstanding recent results in the literature. Finally, examples are given to show the effectiveness of our method and correctness of our results.

No abstract

We employ Lyapunov's second method to investigate uniform asymptotic stability, ultimate boundedness and uniform ultimate boundedness of solutions to certain third-order non-linear differential equations. Our results improve some well-known results in the literature.

In this article, Lyapunov second method is used to obtain criteria for uniform ultimate boundedness and asymptotic behaviour of solutions of nonlinear differential equations of the third order. The results obtained in this investigation include and extend some well known results on third order nonlinear differential equations in the literature.Subjclass [2000] : 34D20, 34D40.