SINGULAR PERTURBATION PROBLEMS USING INDEFINITE LIAPUNOV FUNCTIONS

Abstract

With a system of differential equations consisting of many variables the singular perturbation methods are of great importance. If we know that some variables decrease faster than the others, we can reduce the number of the equations. The reduction makes their solving much more easy. For example, if we use some numerical method, the time and storage necessary for the solu- tions become less than originally [1]. In this paper a singular perturbation problem, the existence and separation of the small, and large solutions of a differential equation is considered, but instead of the usual way an indefinite Liapunov function is used for the investigation.