Uniform-Ultimate Boundedness, Stability and Periodicity of Solutions To Certain Differential Equation of Third Order

Abstract

In this paper, we employ Lyapunov direct method to examine certain necessary and sufficient criteria under which the solutions of the nonlinear third order differential equation considered are uniform-ultimately bounded, stable and possess at least one periodic solution when the nonlinear terms in the equation are differentiable functions of their respective arguments. Two numerical examples and graphical representation of the trajectories of the solutions by Maple Software are given to demonstrate the validity and correctness of obtained results. Specifically, our results include, complement and generalize the results in [1] and some other results in literature. © 2024, MTJPAM Turkey. All rights reserved.