摘要
本文考虑非线性向量边值问题:其中ε是正的小参数,0≤x≤1,f,g是R^4中的连续函数。在适当的假设下,利用微分不等式理论,我们证明了上述问题的解的存在性,并得到包括边界层和内层在内的解的估计.
In this paper, we consider the vector nonlinear boundary value problemt
εy''=F(x,y,z.y',ε). y'(0)=A1, y(1)=B1,
εz''=g(x,y,z,z',ε), z(0)=A2, z(1)=B2.
where ε>0 is a small parameter, 0≤x≤1, f and g are continuous functions in R4. Under appropriate assumptions, by means of the differential inequalities, we demonstrate the existence and estimation, involving boundary and interior layers, of'the solutions to the above problem.
出处
《应用数学和力学》
CSCD
北大核心
1990年第11期999-1005,共7页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助的项目
关键词
边值问题
奇摄动
微分不等式
singular perturbation, differential inequality, boundary layer
