Lyapunov-Schmidt Reduction of Differential-Algebraic Equation

Abstract

In this paper we investigate the asymptotic stability of an equilibrium solution of the differential algebraic equations (DAEs) effected by the Lyapunov-Schimdt reduction. The main conclusion of this paper is that, under the hypothesis , the stability or instability of an equilibrium solution (x0, y0, ) of the DAEs is determined by the sign of DyG where G is the reduced function obtained by the Laipunov-Schimdt reduction.