Ultimate boundedness of the solutions of certain third order nonlinear non-autonomous differential equations

Convergence of Solutions to a Certain Vector Differential Equation of Third Order

“…Thus, it is worthwhile to study the topic for (1). It should be noted that the result to be established here is different from that in Afuwape [2], Afuwape and Omeike [1,3], Olutimo [4], and the above mentioned papers. This paper is an extension and generalization of the result of Afuwape and Omeike [3].…”

“…The author established a new result on the convergence of solutions of (2) under different conditions on the function 𝑃. For some related papers on the convergence of solutions to certain vector differential equations of third order, the readers can referee to the papers of Afuwape [2], Afuwape and Omeike [3], and Olutimo [4]. Further, it is worth mentioning that in a sequence of results Afuwape [2,5,6], Afuwape and Omeike [3], Afuwape and Ukpera [7], Ezeilo [8], Ezeilo and Tejumola [9,10], Meng [11], Olutimo [4], Reissig et al [12], Tiryaki [13], Tunc ¸[ [14][15][16], Tunc ¸and Ates ¸ [17], C. Tunc and E. Tunc ¸ [18], and Tunc ¸and Karakas [19] investigated the qualitative behaviors of solutions, stability, boundedness, uniform boundedness and existence of periodic solutions, and so on, except convergence of solutions, for some kind of vector differential equations of third order.…”

Result on the Convergence Behavior of Solutions of Certain System of Third-Order Nonlinear Differential Equations

“…by extending the result of [17] to the special case ( ) F X AX =   of [17]. Also recently, Olutimo [20] studied the equation…”

“… have been studied by [16] [17]. They have obtained some results related to the convergence properties of solutions as well as Afuwape in [18].…”

On the asymptotic behaviour of solutions of certain differential equations of the third order

“…Notable authors that have contributed immensely to the qualitative behaviour of solutions of third order nonlinear differential equations include Ademola et. al., [1,3,5,6] on uniform stability and boundedness of solutions, Afuwape and Adesina [7], Chukwu [9], Ezeilo [10,11,13], Ezeilo and Tejumola [14], Swick [24], Tejumola [25] and Tunç [26] on boundedness of solutions, Afuwape and Omeike [19], Ogundare [18] and Tunç [28] on convergence of solutions, Omeike [19], Qian [20], Swick [23] and Tunç [27] on asymptotic behaviour of solutions. Most of these works were done with the aid of Lyapunov functions which are either incomplete or contain signum functions.…”