奇摄动问题解的多层现象

Singularly Perturbed Two Points Boundary Value Problems

讨论了一类二阶微分方程奇摄动两点边值问题 .首先求出问题的外部解 ,然后再利用伸长变量 ,构造了对应问题的内部解 ,最后利用匹配原则得到了原问题解的渐近式 ,并且指出了该解的展开式具有多层边界现象 .

The author studies a class of singularly perturbed two points boundary value problem for second order differential equations. First, he finds the outer solution to the problem, then by using the stretched variable he constructs the inner solution to the corresponding problem, and finally, by using the matching principle he obtains the asymptotic expansion of solution to the original problem. And at the same time, he points out that the asymptotic expansion of the solution possesses a multi-layer phenomenon.