具有转向点的奇摄动非线性Robin问题

Singularly Perturbed Nonlinear Robin Problems With Turning Points

本文利用边界层校正法研究了在右端点具有转向点的二阶非线性方程的奇摄动Robin问题 sy″=f(x,y,y′s),-1<x<0、 (1) y(-1,s)-py′(-1,s)=A(s),y(0,s)=B(s), (2)其中s>0是小参数,p>0。在适当的假设下,利用微分不等式作者证明了此Robin问题解的存在性,并得到了其一致有效渐近展式。

The singularly perturbed Robin problems for second order nonlinear differential equations with turning points occurring at the right-hand endpoint, where ε is a small positive parameter and p is a positive constant, are studied with the method of boundary layer correction. Under suitable assumptions of differential inequalities, the existence of the solutions of the Robin problems is proved and the uniformly valid asymptotic expansion is obtained.