带有积分边界条件的奇异摄动边值问题的渐近解  

Asymptotic Solution of Singularly Perturbed Boundary Value Problem with Integral Boundary Condition

作　　者：武利猛[1] 倪明康 李素红[1] 陆海波 Wu Limeng;Ni Mingkang;Li Suhong;Lu Haibo(School of Mathematics and Information Technology,Hebei Normal University of Science and Technology,Hebei Qinhuangdao 066004;School of Mathematical Sciences,East China Normal University,Shanghai 200241;School of Economics and Management,Shanghai Institute of Technology,Shanghai 201418)

机构地区：[1]河北科技师范学院数学与信息科技学院,河北秦皇岛066004 [2]华东师范大学数学科学学院,上海200241 [3]上海应用技术大学经管学院,上海201418

出　　处：《数学物理学报（A辑）》2020年第5期1192-1203,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(11871217,11901152);国家重点研发计划(2019YFC1407903)。

摘　　要：研究了一类带有积分边界条件的奇异摄动边值问题,利用奇异摄动几何理论证明了阶梯状空间对照结构解的存在性.基于解的结构,利用边界层函数法构造了原问题一致有效的形式渐近解.通过一个例子,验证了主要结果.In this paper,we consider a class of singularly perturbed boundary value problem with integral boundary condition.Based on the singularly perturbed geometric theory,the existence of step-like contrast structure solution is proved.By virtue of the structure of the solution,we construct the uniformly valid formal asymptotic solution by the boundary layer function method.Finally,an example is given to show the main result.

关 键 词：奇异摄动 渐近解 边界层函数法 

分 类 号：O175.14[理学—数学]