On singular perturbation method of perturbed bifurcation problems

In this paper, the general mathematical principle is overall explained and a new general technique is presented in order to calculate uniformly asymptotic expansions of solutions of the perturbed bifurcation problem (1.6) in the vicinity of y=0, =0, =0, by means of singular perturbation method. Simultaneously, Newton's polygon^4] is generalized. Finally, the calculating results of two examples are given.Presented to the Symposium on Bifurcation, Catastrophe and Stability (New. 1983) Held in Wuhan. This article was communicated by Prof. Wang Ren — Ed.