一类高阶方程的奇摄动边值问题

A Class of Singularly Perturbed Boundary Value Problems for Higher Order Equations

在适当条件下,对一类具非线性边界条件的高阶方程的奇摄动问题,通过引入非常规的渐近序列,运用合成展开法,构造问题的形式渐近解,再运用微分不等式理论证明原问题解的存在性及所得形式渐近解的一致有效性.

Under certain conditions,the formal asymptotic solutions are constructed for a class of singularly perturbed problems for higher order equations with nonlinear boundary value conditions by the introduction of the unconventional asymptotic sequence and the meth- od of composite expansion. Then the existence of solutions for the original problems and the uniform validity of the formal asymptotic solutions are proved by the theory of differential inequality.