A NEW INSTABILITY RESULT ON THE SOLUTIONS OF NONLINEAR VECTOR DIFFERENTIAL EQUATIONS OF THE FIFTH ORDER

BEŞINCI MERTEBEDEN LİNEER OLMAYAN VEKTÖR DIFERENSIYEL DENKLEMLERİN ÇÖZÜMLERİNİN KARARSIZLIĞI ÜZERINE YENİ BİR SONUÇ

Melike KARTA

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 a new instability result and also to give an example indicate the importance of the topic. Related to a scalar differential equation mentioned in the literature, the findings of this study are beneficial for result of instability of the trivial solution of five order non-linear vectoral differential equations.

Özet

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Keywords: Kararsızlık, Krasovskii kriteri, Lyapunov’un ikinci