一类带大参数的具有2n阶转向点的奇摄动方程

摘要

A class of singularly perturbed ordinary differential equation for larger parameter with 2n order turning point is considered.Using the Liouville-Green transform and the first class of the Bessel function of 1/(2(n+1)) order,the outer solution and the interior layer solution are constructed.Finally,the matching conditions are obtained by the matching principle,and then,the different representations for the uniformly asymptotically approximated solution in the entire area are obtained.%文章讨论了一类带有大参数的具有2n阶转向点的常微分方程.分别利用Liouville-Green变换和1/（2（n＋1））阶第一类Bessel函数,构造了方程的外部解和内层解,最后通过匹配原理得到了方程外部解和内层解可匹配的条件,从而得到方程在整个区间上有效的不同渐近近似式.