某类奇摄动边值问题解的多重边界层现象

Multiple Boundary Layer Phenomena of Solution for Singularly Perturbed Boundary Value Problem

本文揭示了某类四阶半线性常微分方程边值问题解的多重边界层现象,根据不同的层次用不同的伸长变量,分别构造了具有不同量级的边界层校正项,并给出证明摄动问题解存在的充分条件,从而证得关于解的一致有效的渐近展开式和有关的余项估计。

In this paper the author revealed the multiple boundary layer phenomena of solution of boundary value problem for a fourth order semilinear ordinary differential equation. According to the various layer sequence he used various stretch variables and respectively constructed boundary layer correction terms with various quantitative order, and the sufficient conditions of existence of solution are given. Thereby, the uniformly valid asymptotic expansion of solution and the estimation of corresponding to the remainder term are obtained.