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
计量
- 文章访问数: 2608
- HTML全文浏览量: 102
- PDF下载量: 622
- 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

HTML全文

参考文献(13)

[1]	Sficas,Ntouyas.A boundary value problems for nth order functional differential equation[J].Nonlinear Anal,1981,5(3):325-335.
[2]	Regan D O.Existence of solution to some retarded functional differential equation[J].Nonlinear Anal,1993,20(2):79-95.
[3]	Laui B S,Zhang B G.Boundary value problems for second order functional differential equations[J].Ann Differential Equations,1992,8(3):261-268.
[4]	LU Shi-ping.Boundary value problems for nth order retarded functional differential equation[J].Ann DifferentialEquations,1999,15(3):298-304.
[5]	鲁世平.n阶泛函微分方程边值问题[J].数学研究与评论,,2000,20(30):411-415.
[6]	Henderson J,Yin W.Positive solutions and nonlinear eigenvalue problems for functional differential equation[J].Applied Mathematics Letters,1999,12(1):63-68.
[7]	Lange C G,Miura R M.Singular perturbation analysis of boundary value problem for differential difference equations[J].SIAMAppl Math,1982,42(3):502-503.
[8]	MIAO Shu-mei,ZHOU Qin-de.The asymptotic expansions of singularly perturbed boundary value problems for semilinear differential difference equations[J].Northeastern Math,1989,5(3):283-293.
[9]	周钦德,苗树梅.关于微分差分方程边值问题[J].数学学报,1989,32(1):55-70.
[10]	LU Shi-ping.A kind of singularly perturbed boundary value problems for Volterra functional differential equations[J].Ann Differential Equations,1998,14(2):247-253.
[11]	LU Shi-ping.A kind of singularly pertubed boundary value problem for nonlinear Volterra functional differential equations[J].Appl Math J Chinese Univ,Ser B,2000,15(2):137-142.
[12]	Erber L H.Nonlinear boundary value problems for second order differential equations[J].J Differential Equaitons,1970,7(2):459-472.
[13]	Hale J.Theory of Functional Differential Equations[M].New York:Springer Verlag,1977.