摘要
本文研究含两个小参数ε>0和μ>0的二阶半线性微分方程的边值问题采用两阶段展开方法分别对ε/μ~2→0(μ→0),μ~2/ε→0(ε→0)和ε=μ~2三种情形构造出解的形式展式,利用微分不等式方法证明了解的存在唯一性并给出余项的一致有效估计。
The paper covers the singularly perturbed boundary value problems for semilinear second order ordinary differential equations with two small parameters δ>0 and μ>0:For the three cases that δ/μ~2 →0 (μ→0),μ~2/δ→0 (δ→0)andδ=μ~2, the formal asymptotic expansions of solution are constructed by two steps and the existence and uniqueness of solution are proved by using the differential inequality method, in addition, the uniformly valid estimates of remainder are given as well.
出处
《吉林大学自然科学学报》
CAS
CSCD
1991年第4期37-45,共9页
Acta Scientiarum Naturalium Universitatis Jilinensis
基金
国家自然科学基金
关键词
常微分方程
边值
奇摄动
参数
解
singular perturbation, boundary value problem, asymptotic expansion of solution
