一类具有三个转向点的大参数奇摄动问题(英文)

A Class of Singularly Perturbed Equations for Larger Parameter with Three Turning Points

文中研究了一类具有三个转向点的大参数奇摄动方程的渐近解.首先利用Liouville-Green变换构造方程在不同区域的外部解.然后利用1/3阶和-1/3阶Bessel函数,分别构造出方程在三个转向点附近的内层解.最后利用匹配原理得到外部解和内层解中任意常数满足的匹配条件.

A class of singularly perturbed problem for larger parameter with three turning point is considered.Firstly,the outer solution in different areasis obtained using the Liouville-Green transform.Then,introducing stretching transform and using the Bessel function of 1/3 and-1/3 order the interior layer solution near the x=a1,x=a2 and x=a3is constructed respectively.Finally,the arbitrary constants is selected for the outer solution and interior layer solution using the matching principle.