Sains Malaysiana 40(12)(2011): 1455–1459

On the Instability of Solutions of Nonlinear Delay Differential Equations of Fourth and Fifth Order

(Kestabilan Penyelesaian Persamaan Pembezaan Tunda Tak Linear Tertib ke Empat dan Lima)

Cemil Tunç*

Department of Mathematics, Faculty of Sciences, Yüzüncü Yıl University

65080, Van –Turkey

Received: 9 December 2010 / Accepted: 2 March 2011

ABSTRACT

The main purpose of this paper is to introduce some new instability theorems related to certain fourth and fifth order nonlinear differential equations with a constant delay. By means of the Lyapunov-Krasovskii functional approach, we obtained two new results on the topic.

Keywords: Delay differential equation; fourth and fifth order; instability; Lyapunov-Krasovskii functional

ABSTRAK

Objektif utama artikel ini ialah untuk memperkenalkan beberapa teorem ketakstabilan yang baru berkaitan dengan persamaan pembezaan tak linear tertib ke empat dan lima dengan tundaan malar. Melalui pendekatan fungsi Lyapunov-Krasovskii, dua keputusan baru dalam topic ini telah diperoleh.

Kata kunci: Fungsi Lyapunov-Krasovskii; ketakstabilan; persamaan pembezaan tunda; tertib ke empat dan lima

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*Corresponding author; email: cemtunc@yahoo.com