非线性微分方程边值问题的奇摄动

Singular Perturbation for Nonlinear Boundary Value Problems of Differential Equation

本文研究了非线性边值问题: εy″-f(x,y,y′)=0,0<x<1,0<ε<<1, y(0)=A, y(1)=B.在f_(y′)≥0或f_(y′)≤0的情形下,利用微分不等式理论得到了上述边值问题解的存在性定理及解的估计式。

In this paper, the nonlinear boundary value problem: is considered. Under the condition fy≥0 or fy'≤0, using the differential inequalities there exists a solution of the above problem and we obtained the estimation of the solution.