具有无穷大边界值的半线性奇摄动Robin问题

Robin Problem With Infinite Boundary Values for Singularly Perturbed Semi-linear Differential Equations

文章研究一类具有无穷大边值的二阶半线性微分方程的奇摄动Robin问题的双边界层与内层现象。基于边界层校正,构造了该问题的边界层、内层校正函数;基于微分不等式理论,证明了该边值问题解的存在性,同时得到解的一致有效的高阶渐近估计。

The phenomenons of double-boundary layers and interior layer of Robin problem with infinite boundary values for semi-linear singularly perturbed differential equations are studied in this paper.Combining the method of error estimation, the boundary layer function and the interior layer function are obtained; the existence and the uniform validity with high order for the solution are proved by the differential inequality.