Asymptotic Stability of Singular Ordinary Differential Equation Established Via Extended System Reduction

In this paper we discuss the stability of an equilibrium solution of ODE effected bythe extended system reduction. The main conclusion of this paper is that, under thehypothesis rank(DF)(yo,0) = n — 1, the stability or instability of an equilibrium solution (y0,0) of y = F(y, a) is determined by the sign of DG where G is the reduced function obtained by the extended system reduction. Also the stability of a small amplitude periodic solution of ordinary differential equation y = F(y, a) is discussed by the same way.