摘要
本文应用上、下解方法研究如下四阶非线性奇摄动边值问题。ε~2y~(4)=f(x,y,y′,y″,ε)0<x<1y(0)=A_1(ε),y(1)=B_1(ε)y″(0)=A_2(ε),y″(1)=B_2(ε)ε为止的小参数,在一定的条件下,构造出包括外部解和边界层项的形式展式,并证明其一致有效性。
In this paper,we consider the following singularly perturbed problem: ε~2y~(4)=f(x,y,y′,y″,ε)0<x<1 y(0)=A_1(ε),y(1)=B_1(ε) y″(0)=A_2(ε),y″(1)=B_2(ε) where ε is a small positive parameter.Under some suitable assumptions,using sub-and super-solutions the author obtains the estimate of a solution of the original problem.
基金
国家自然科学基金
关键词
非线性
微分方程
边值问题
奇摄动
Fourth order nonlinear differential equations
Sub-and super-solutions
Singular percturbation probbem
