A Note on Boundedness of Solutions To A Class of Non-Autonomous Differential Equations of Second Order

Abstract

By defining some appropriate Liapunov functions, we discuss boundedness of solutions to a class of non-autonomous and nonlinear differential equations of second order. In this work, we prove some results established in the literature by Liapunov's second method instead of the integral test. We give six examples to illustrate the theoretical analysis in this work and effectiveness of the method utilized here.