On the Stability of Solutions of Nonlinear Functional Differential Equation of the Fifth-Order - Advances in Pure Mathematics

APM > Vol.4 No.8, August 2014

On the Stability of Solutions of Nonlinear Functional Differential Equation of the Fifth-Order ()

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DOI: 10.4236/apm.2014.48046 3,666 Downloads 4,708 Views

Author(s)

A. M. A. Abou-El-Ela, A. I. Sadek, A. M. Mahmoud, R. O. A. Taie

Affiliation(s)

Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt.
Department of Mathematics, Faculty of Science, New Valley Branch, Assiut University, New Valley, El-Khargah, Egypt.

ABSTRACT

The main purpose of this paper is to investigate global asymptotic stability of the zero solution of the fifth-order nonlinear delay differential equation on the following form

By constructing a Lyapunov functional, sufficient conditions for the stability of the zero solution of this equation are established.

KEYWORDS

Global Asymptotic Stability, Lyapunov Functional, Fifth-Order Delay Differential Equations

Share and Cite:

Abou-El-Ela, A. , Sadek, A. , Mahmoud, A. and Taie, R. (2014) On the Stability of Solutions of Nonlinear Functional Differential Equation of the Fifth-Order. Advances in Pure Mathematics, 4, 357-367. doi: 10.4236/apm.2014.48046.

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