ON BEHAVIOUR OF SOLUTIONS TO SOME SYSTEMS OF SECOND ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

ON BEHAVIOUR OF SOLUTIONS TO SOME SYSTEMS

Abstract

The essence of this paper is to determine certain set of conditions on the nonlinear terms appearing in some second order nonlinear ordinary and stochastic differential equations  with and without delay,  such that  stability and boundedness of their solutions are ensured.  We construct appropriate Lyapunov function and functional as tools for the establishment of our results. A special case of a second-order differential equation is provided as an example to validate our hypotheses and demonstrate the reliability and effectiveness of the technique used. Our results improve and generalize many results in literature like those in \cite{Adm}, \cite{o2}.