关于摄动分支问题的奇异摄动法

本文较全面地阐述了用奇异摄动法计算摄动分支问题(1.6)在y=0,λ=0,δ=0附近的解的一致渐近展式的一般数学原理和方法,并推广了牛顿多边形原理。最后,给出了两个计算实例。

On Singular Perturbation Method of Perturbed Bifurcation Problems

In this paper, the general mathematical principle is over-all 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, λ=0,δ=0, by means of singular perturbation method. Simultaneously, Newton's polygon4] is generalized. Finally, the calculating results of two examples are given.