一类高阶拟线性方程两点边值问题的奇摄动

SINGULAR PERTURBATION OF SOME HIGHER ORDER QUASILINEAR TWO POINTS BOUNDARY VALUE PROBLEMS

本文考虑高阶拟线性微分方程边值问题:εy^(n)=f_1(t,ε,y,……,y^((n-2)))y^((n-1))+f_2(t,ε,y,……,y^((n-2)))0<t<1 (1)y^(j)(0,ε)=A_J(ε) j=0,1……,n-2 (2)y^((n-2))(1,ε)=B(ε) (3)这里ε为小的正参数。上述问题有许多作者对n=2,3,的情形进行过研究,至于高阶非线性情形,Howes也曾进行了讨论,但他只对问题解与退化解之差作出估计。本文是在此基础上,应用边界层校正法和高阶微分不等式的技巧,得到包括边界层在内的任意次近似的一致有效的渐近解。

In this paper, we consider the boundary value problem: where ε is a small positive parameter. Under some suitable assumptions, using the method of 'boundary layer corrections' and the differential inequality techniques, we obtain an uniformly efficient asymptotic solution which includes the boundary layer and can be approximated any times.