奇摄动高阶微分方程边值问题的套层解

Jacketed Solution of Boundary Value Problem for Singularly Perturbed Higher Order Differential Equation

研究一类高阶微分方程两点边值问题的奇摄动,揭示了其解分别在两端点呈现双重边界层的性质.根据不同的层次,引进不同量级的伸长变量,分别构造了不同量级的边界层校正项,并利用微分不等式理论,得到了解的一致有效的渐近展开式.

We study the singular perturbation of boundary value problem for a class of higher order ordinary differential equation, the solution is shown to exhibit double layer behavior. By introducting extended variable and using the theory of differential inequality, we obtain the uniformly effective asymptotic expansion.