具非线性边界条件的Volterra型泛函微分方程边值问题奇摄动

鲁世平

具非线性边界条件的Volterra型泛函微分方程边值问题奇摄动

鲁世平

安徽师范大学数学系, 安徽芜湖 241000

基金项目: 安徽省教育厅自然科学基金资助项目(2002kj133)

详细信息

作者简介:
鲁世平(1962- ),男,安徽无为人,副教授,博士(E-mail:lushioing26@sohu.com).

中图分类号: O175.7
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- 被引次数: 0
出版历程
- 收稿日期: 2001-06-07
- 修回日期: 2003-05-13
- 刊出日期: 2003-12-15

Singularly Perturbed Nonlinear Boundary Value Problem for a Kind of Volterra Type Functional Differential Equation

LU Shi-ping

Department of Mathematics, Anhui Normal University, Wuhu, Anhui 241000, P. R. China

摘要

摘要: 首先利用微分不等式理论和一些分析技巧,探讨了一类具非线性边界条件的二阶Volterra型泛函微分方程边值问题解的存在性问题.然后通过对右端边界层函数和外部解的构造,进一步研究了一类具小参数的二阶Votterra型非线性边值问题.利用微分中值定理和上、下解方法得到了边值问题解的存在性,并给出了解的关于小参数的一致有效渐近展开式.
- 奇异摄动 /
- 泛函微分方程 /
- 边值问题 /
- 一致有效渐近展开式
Abstract: By employing the theory of differential inequality and some analysis methods, a nonlinear boundary value problem subject to a general kind of second order Volterra functional differential equation was considered first. Then, by constructing the right-side layer function and the outer solution, a nonlinear boundary value problem subject to a kind of second order Volterra functional differential equation with a small parameter was studied further. By using the differential mean value theorem and the technique of upper and lower solution, a new result on the existence of the solutions to the boundary value problem is obtained, and a uniformly valid asymptotic expansions of the solution is given as well.
- singular perturbation /
- functional differential equation /
- boundary value problem /
- uniformly valid asymptotic expansion

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参考文献(13)

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