ICGST- ACSE Journal

ACSE Volume (9) - Issue (I) ICGST
Stability and Boundedness of Solutions of Certain Third-Order Non-Linear Delay Differential Equation

A. M. A. Abou-El-Ela(1), A. I. Sadek(1), A. M. Mahmoud (2)
(1) Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt
(2) Department of Science and Mathematics, Faculty of Education, Assiut University, New Valley, El-khargah 72111, Egypt.

 

Abstract
This article presents sufficient conditions for the uniform stability of the zero solution when p equals zero, the uniform boundedness and uniform ultimate boundedness of all solutions in case p does not equal zero of the third-order nonlinear delay differential equation (1). By constructing Lyapunov functionals we achieved new contribution which includes and improves some related results existing in the relevant literature.

Keywords: Lyapunov functional, Stability, Boundedness, Third-order delay differential equations.

(P1110842411, 416 KB)

@ARTICLE{P1110842411,

AUTHOR = {A. M. A. Abou-El-Ela, A. I. Sadek, A. M. Mahmoud},

TITLE = {Stability and Boundedness of Solutions of Certain Third-Order Non-Linear Delay Differential Equation},

JOURNAL = {ICGST International Journal on Automatic Control and Systems Engineering, ACSE},

YEAR = {2009},

VOLUME = {09},

ISSUE = {I},

PAGES={9-- 15}

}

(P1110842411, 416 KB)