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Discrete Dynamics in Nature and Society
Volume 2008, Article ID 971534, 6 pages
Research Article

A New Instability Result to Nonlinear Vector Differential Equations of Fifth Order

1Department of Mathematics, Faculty of Arts and Sciences, Yüzüncü Yıl University, 65080 Van, Turkey
2Institute of Sciences, Yüzüncü Yıl University, 65080 Van, Turkey

Received 20 May 2008; Accepted 9 July 2008

Academic Editor: Binggen Zhang

Copyright © 2008 Cemil Tunç and Melike Karta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By constructing a Lyapunov function, a new instability result is established, which guarantees that the trivial solution of a certain nonlinear vector differential equation of the fifth order is unstable. An example is also given to illustrate the importance of the result obtained. By this way, our findings improve an instability result related to a scalar differential equation in the literature to instability of the trivial solution to the afore-mentioned differential equation.