具有二阶转向点的大参数奇摄动方程

讨论了一类二阶常微分方程并具有高阶转向点的大参数的奇异摄动问题．首先将方程同时作自变量和因变量的Liouville-Green变换,得到问题的外部解．然后引入伸展变量变换。并利用1／4和-1／4阶Bessel函数，构造在转向点附近的内层解．最后从解在不同区域的表示式,利用匹配原理适当地选取任意常数。将外部解和内层解进行匹配得到问题解的匹配条件．从而得到在整个区域内的一致有效的渐近解的不同表示式．

Singularly Perturbed Equations for Larger Parameter with Second Order Turning Point

In this paper,a class of singularly perturbed problem for ordinary differential equation of second with higher order turning point is considered. Firstly,introducing the Liouville-Green transform for the independent variable and function, the outer solution is obtained. Then,introducing stretching transform and using the Bessel functions of 1/4 and -1/4 order, the interior layer solution is constructed. Finally,from the representations of solution in different regions and using the matching principle, appropriate selecting arbitrary constants and matching the outer solution and interior layer solution,the matching conditions for the solution of problem is found. And then, the different representations for the uniformly valid asymptotic solution in the entire area are obtained.