STABILITY AND BOUNDEDNESS OF SOLUTIONS OF NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS WITH BOUNDED DELAY

Author:

KORKMAZ Erdal1,ÖZDEMİR Abdulhamit2

Affiliation:

1. Mus Alparslan Universty

2. MUŞ ALPARSLAN ÜNİVERSİTESİ

Abstract

In this paper, we investigate the boundedness and uniformly asymtotically stability of the solutions to a certain third order non-autonomous differential equations with bounded delay. By constructing a Lyapunov functional, sufficient conditions for the stability and boundedness of solutions for equations considered are obtained. We used an example to demonstrate the feasibility of our results. The results obtain essentially improve, include and complement the results in the literature.

Publisher

Journal of Mathematical Sciences and Modelling

Subject

Materials Chemistry,Economics and Econometrics,Media Technology,Forestry

Reference33 articles.

1. \bibitem{1} T. A. Ademola, P. O. Arawomo, Asymptotic behaviour of solutions of third order nonlinear differential equations, \emph{Acta Univ. Sapientiae Math.} \textbf{3} (2011), 197--211.

2. \bibitem{2} T. A. Burton, \textit{Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Mathematics in Science and Engineering Vol. 178}, Academic Press, Orlando, 1985.

3. \bibitem{3} L. \`{E}. \`{E}l'sgol'ts, \textit{Introduction to the theory of differential equations with deviating arguments}, Translated from the Russian by Robert J. McLaughlin Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1966.

4. \bibitem{4} L. \`{E}. \`{E}l'sgol'ts, S. B. Norkin, \textit{Introduction to the theory and application of differential equations with deviating arguments}, Translated from the Russian by John L. Casti. Mathematics in Science and Engineering, Vol. 105. Academic Press [A Subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1973.

5. \bibitem{5} J. O. C. Ezeilo, On the stability of solutions of certain differential equations of the third order, \emph{Quart. J. Math. Oxford Ser. } \textbf{11}(2) (1960), 64-69.

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