Stability and Boundedness of Solutions of Non-Autonomous Differential Equations of Second Order

Abstract

This paper establishes some new sufficient conditions to ensure the stability and boundedness of solutions of certain second order non-autonomous and non-linear differential equations. By defining two appropriate Liapunov functions, we obtain three new results on the subject and give some examples to illustrate the theoretical analysis in this work. By this work, as well as two new results, we also extend and improve an important result from the literature.