An instability theorem for a certain fifth-order delay differential equation

Abstract

Text of the abstract. The main purpose of this paper is to introduce a new instability theorem related to a fifth order nonlinear differential equation with a constant delay. By means of the Lyapunov-Krasovskii ([8], [13]) functional approach, we obtain a new result on the topic.

A New Instability Result on the Solutions of Nonlinear Vector Differential Equations of the Fifth Order

“…In addition, respectively, (Tunç 2004(Tunç , 2005 investigated the instability of trivial solution of the fifth order vector differential equations of the form EÜFBED -Fen Bilimleri Enstitüsü Dergisi Cilt-Sayı: 8-2 Yıl: 2015 248-258 and (Tunç & Şevli 2008) showed a similar study for the instability of trivial solution of the fifth order vector differential equation (Tunç & Karta 2008) analyzed sufficient conditions which ensure the trivial solution of vector differential equation…”

“…About the topic, we refer to the papers of (Ezeilo 1978(Ezeilo , 1979, (Tiryaki 1987), (Li & Yu 1990), (Li & Duan 2000), (Sadek 2003), (Tunç 2004(Tunç , 2005, (Tunç & Şevli 2008), (Tunç & Karta 2008), (Krasovskii 1955). In all of the papers mentioned above, authors used Krasovskii's criteria (1955) and Lyapunov's second (or direct) method (1966).…”

“…In addition, for some related contributors to the subject, we refer to the papers of (Tunç 2004(Tunç , 2013. In all of the above mentioned papers, authors took into consideration of Krasovskii 's criteria (1955) and Lapunov's second (or direct) method (1993).…”

Instability of a Fifth-Order Nonlinear Vector Delay Differential Equation with Multiple Deviating Arguments

“…Lyapunov functions and functionals have been successfully used and are still being used to obtain stability, instability, boundedness, and the existence of periodic solutions of differential equations, differential equations with functional delays, and functional differential equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]).…”

Instability of Non-Linear Functional Differential Equations of Fifth Order

“…However, from then on, the Lyapunov's direct method was also widely used and is still being employed to study the instability of solutions of ordinary differential equations and functional differential equations of fifth order, see e.g. Tunç [1][2][3][4][5][6][7][8][9][10], Li and Duan [11], Ezeilo [12][13][14], Li and Yu [15], Sadek [16], Sun and Hou [17], Tiryaki [18], Tunç and Erdogan [19], Tunç and Karta [20], and Tunç and Şevli [21] and the references therein. Besides, it is worth mentioning that to the best of our knowledge, the instability of the solutions of certain functional differential equations of the fifth order has been discussed in the literature, recently (see [1][2][3][4][5][6][7]).…”