奇摄动非线性系统Robin边值问题

Singularly Perturbed Robin Boundary Value Problems for Nonlinear Systems

本文研究了非线性系统奇摄动问题：ε2y"－（x，y，y）＝0，0＜x＜1，0＜ε≤1，y（0）－py'（0）＝A，p＞0，y（1）＝B，其中y，f，A，B为n维向量．在相应的假设下，利用代数型边界层函数，证明了该问题存在一个解y（x，ε），并利用微分不等式方法得到了其解的渐近估计．

The singularly perturbed nonlinear system ε2y'-f(x, y,y')=0, 0<x<1,0<ε≤1,y (0) -py' (0)=A,p>0,y(1)=B, where y,f,A , B are n-dimensional vectors is considered. Under the appropriate assumptions,using the algebraic boundary layer functions, the author proved that there exists a solution y(x,ε) and the estimation of y(x,ε) is obtained using the method of differential inequalities.