New Boundedness Results for Solutions of Second Order Non-Autonomous Delay Differential Equations

Abstract

We study the boundedness of solutions of some second order non-autonomous delay differential equations by the Liapunov functional approach. We establish three new results which include sufficient conditions for the solutions of the equations considered to be bounded. By this work, we improve some boundedness results in the literature, which were obtained on certain second order ordinary differential equations without delay, to the boundedness of the solutions of some second order non-autonomous delay differential equations.