New Instability Results on Certain Fifth Order Nonlinear Vector Differential Equations

Abstract

The purpose of this paper is to investigate instability of the trivial solution of non-linear vector differential equation of the fifth order by constructing a Lyapunov function to get two new instability results. Also, for each result an example is given to indicate the importance of the topic.Related to a scalar differential equations mentioned in the literature, the findings of this study are beneficial for results of instability of the trivial solution of five order non-linear vectoral diferential equations.

Key words: Nonlinear vector differential equation of fifth, Lyapunov function, instability.