Criteria for the asymptotic behaviour of solutions to certain third-order nonlinear differential equations

Abstract

We investigate and provide sufficient criteria for ultimate boundedness of solutions as well as the asymptotic stability of the trivial solution to certain nonlinear differential equation of order three. Using the Lyapunov second method and the Yoshizawa limit point approach, we establish our results. The equation considered is new and more general. Hence, our results are new, generalized and improved on some earlier established results. In order to verify the correctness of our obtained results, a numerical example is provided with the trajectories of the solutions.