Instability results for certain systems of fourth and fifth order differential equations

Instability to nonlinear vector dierential equations of fth order with constant delay

“…It should be noted that since 1978 till now the instability of the solutions of certain scalar differential equations of the fifth order without and with delay and vector differential equations of the fifth order without delay was discussed in the literature. For a comprehensive treatment of the subject, we refer the readers to the papers of Ezeilo [2], Sadek [5], Sun and Hou [6], Tunç ([7]- [14]), Tunç and Erdogan [15], Tunç and Karta [16], Tunç and Şevli [17] and the references cited in these sources. However, a review to date of the literature indicates that the instability of solutions of vector differential equations of the fifth order with delay has not been investigated.…”

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

“…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).…”

“…On the other hand, Sadek (2003) examined the instability of trivial solutions of the fifth order vector differential equations described as…”

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]).…”