Stability and boundedness for a kind of non-autonomous differential equations with constant delay

Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments

“…(vii) If = 1 and ( ) = then (3) coincides with (2) discussed in [27]; hence our hypotheses coincide with that of Tunç in [27].…”

“…, ) exist and are continuous for all and with ℎ (0) = 0. This work is motivated by the recent works in [9,27]. Our results are new; in fact according to our observation from relevant literature, this is the first paper where both the functions and the forcing term contain sum of multiple deviating arguments.…”

“…Recently, Tunç [27] employed Lyapunov's second method to prove two results on stability and boundedness of nonautonomous differential equations with constant delay (1) Furthermore, Ademola [9] discussed existence and uniqueness of a periodic solution to the third-order differential equation Unfortunately, the problem of uniform asymptotic stability, uniform ultimate boundedness, and existence and uniqueness of periodic solutions of the third-order delay differential equation (3), where all the nonlinear terms (specifically, the forcing term and the function ) are sum of multiple deviating arguments, is yet to be investigated. This is not unconnected with the difficulties associated with the construction of suitable complete Lyapunov functional.…”

On the stability and boundedness of certain third order non-autonomous differential equations of retarded type

“…Besides, qualitative properties of solutions of third order differential equations such as stability, instability, boundedness, oscillation, and periodicity of solutions have been studied by many authors; in this regard, we refer the reader to the monograph by Reissig et al [17], and the recent papers of Adams et al [1], Ademola and Arawomo [2], Afuwape and Adesina [3], Bai and Guo [5], Ogundare and Okecha [15], Rauch [16], Sadek [18], Tunç ([20]- [27]), Zhang and Yu [29] and the references cited therein. However, to the best of our knowledge, there exist few results on the mentioned qualitative behaviors of solutions for the non-autonomous third order differential equations of retarded type (see, the references of this paper).…”

On the qualitative properties of differential equations of third order with retarded argument

“…al. [3], Chukwu [7], Ezeilo ([12], [13]), Hara [16], Mehri and Shadman [20], Meng [21], Omeike and Afuwape [22], Qian [23], Rauch [24], Smith [26], Swick [27], Tejumola [28], Tunc [29][30][31][32][33][34][35][36][37][38][39][40], Tunc and Ates [41], Tunc and Ergören [42], Wall and Moe [43], Zhang and Yu [44] and references therein). It is well known that an important tool in the study of stability/instability/boundedness/ ultimately boundedness of solutions of the considerable number of ordinary/neutral/retarded differential equations of higher order is the Liapunov function/Liapunov-Krasovskii functional techniques.…”