Boundedness Results for Solutions of Certain Second Order Non-Autonomous Ordinary Differential Equations

Abstract

We consider the second order non-autonomous nonlinear ordinary differential equations of the formwhere , , , , , , and p are real valued functions which depend at most on the argument displayed explicitly.In this research, different forms of integral inequalities and two forms of mean value theorem for integrals without the use of the Lyapunov direct method will be applied to investigate the boundedness of all solutions and their derivative.The results obtained improve some earlier results in the literature.An example with graphical representation using Maple is hereby stated to corroborate the results.