On the ψ-exponential asymptotic stability of nonlinear systems of differential equations

Abstract

Abstract. In this paper we prove sufficient conditions for Ψ-exponential asymptotic stability in variation on R+ of trivial solution of the system x ′ = F (t, x) and for Ψ-exponential asymptotic stability on R+ of trivial solution of the systemMathematics Subject Classification 2010: 34D10, 34D05.

Ψ -asymptotic stability of non-linear matrix Lyapunov systems

“…This paper extends some of the results of Ψ-asymptotic stability of trivial solutions of linear equations (Theorem 1 and Theorem 2)in Diamandescu [4] to matrix Lyapunov systems.…”

“…Later Morchalo [6] introduced the concepts of Ψ-(uniform) stability, Ψ-asymptotic stability of trivial solutions of linear and non-linear systems of differential equations. Further, these concepts are extended to non-linear volterra integro-differential equations by Diamandescu [[3], [4]]. Recently, Murty and Suresh Kumar [ [7], [8]] extended the concepts of Ψ-boundedness, Ψ-stability and Ψ-instability to matrix Lyapunov systems.…”