Convergence of Solutions of Certain Fourth-Order Nonlinear Differential Equations

Abstract

We give sufficient criteria for the existence of convergence of solutions for a certain class of fourth-order nonlinear differential equations using Lyapunov's second method. A complete Lyapunov function is employed in this work which makes the results to include and improve some existing results in literature.

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.…”