CONSTRUCTION OF SUITABLE LYAPUNOV FUNCTIONS FOR SYSTEMS OF LINEAR AND NONLINEAR DIFFERENTIAL EQUATIONS WITH STABILITY OF THEIR TRIVIAL SOLUTIONS

Abstract

In this paper, suitable Lyapunov functions are constructed for systems of linear and nonlinear differential equations. The Lyapunov functions constructed are tested for the stability of the trivial solutions for the  stated problems and the results show that the trivial solution of the linear system of differential equations is asymptotically stable while the trivial solution of the nonlinear system of differential equations is stable (in the sense of Lyapunov). The scientific implication of these results is that the solutions starting near the zero solution for asymptotic stability eventually result to the zero solution in a limit as while solutions starting near the zero solution for Lyapunov stability stay close to the zero solution