Stability Results for the Solutions of Certain Non-Autonomous Differential Equations of Fifth -Order

Abstract

The paper is concerned with the stability of solutions of a class of general type fifth order non-autonomous differential equations (1.3) and (1.4). It is shown that under some less restrictive conditions that all solutions of (1.3) and (1.4) tend to zero as t → ∞. Our results improve that the results obtained by Sadek [9].

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

“…x (5) (t) + A 1 x (4) where x ∈ , t ∈ + , + = [0, ∞), A 1 , A 2 , A 3 , A 4 and A 5 are not necessarily constants. For a comprehensive treatment of the subject we refer the reader to the papers of Ezeilo [4][5][6], Li and Duan [10], Li and Yu [11], Sadek [14], Sun and Hou [15], Tiryaki [16], Tunç [17][18][19], Tunç and Erdogan [21], Tunç and Karta [22], Tunç and Şevli [23] and the references cited in these papers for some works performed on the subject, which include some fifth order nonlinear differential equations without delay.…”

Instability of Certain Nonlinear Differential Equations of Fifth Order

“…In this direction, in recent years, Ezeilo [1]- [3], Li and Duan [6], Li and Yu [7], Sadek [8], Sun and Hou [9], Tejumola [10], Tunc [11]- [13], [15], Tunc and Erdogan [16], Tunc and Karta [17], Tunc and Şevli [18], etc., continued to discuss the existence, non-existence of periodic solutions and instability of solutions to certain nonlinear scalar and vector differential equations of fifth order by the Lyapunov's second method. These researchers obtained many new and considerable results concerning to the mentioned topics.…”

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]).…”