具有不连续系数的三阶半线性奇异摄动边值问题

doi:10.3969/j.issn.1000-5641.2017.02.003

华东师范大学学报(自然科学版) ›› 2017, Vol. 2017 ›› Issue (2): 20-28.doi: 10.3969/j.issn.1000-5641.2017.02.003

具有不连续系数的三阶半线性奇异摄动边值问题

薛虎, 谢峰

东华大学应用数学系, 上海 201620

收稿日期:2016-01-06 出版日期:2017-03-25 发布日期:2017-03-23
通讯作者: 谢峰,男,教授,研究方向为奇异摄动理论及其应用.E-mail:fxie@dhu.edu.cn E-mail:fxie@dhu.edu.cn
作者简介:薛虎,男,硕士研究生,研究方向为奇异摄动理论.E-mail:13918501496@163.com
基金资助:
上海市自然科学基金（15ZR1400800）

Singularly perturbed third-order semilinear boundary value problems with discontinuous coefficients

XUE Hu, XIE Feng

Department of Applied Mathematics, Donghua University, Shanghai 201620, China

Received:2016-01-06 Online:2017-03-25 Published:2017-03-23

摘要/Abstract

摘要：

主要研究了一类具有不连续系数的奇异摄动边值问题解的存在性和渐近估计.首先，利用Schauder不动点定理，建立一般问题的上下解定理；其次，利用边界函数法，构造出形式渐近解，并基于已确立的上下解定理，证明解的存在性和一致有效性；最后给出实例验证主要结论.

关键词: 奇异摄动, 不连续系数, 上下解

Abstract:

The existence and asymptotic estimates of solutions for a class of singularly perturbed boundary value problems with discontinuous coefficients are investigated in this paper. Firstly, by using the Schauder fixed point theorem, a theorem of lower-upper solutions for general problems is established. Secondly, the formal asymptotic solution is constructed by the method of boundary functions, and the existence and uniform validity of the solution are proved by using the theorem of lower-upper solutions. Finally, an example is presented as an illustration.

Key words: singular perturbation, discontinuous coefficients, lower-upper solutions

中图分类号:

O175.14

薛虎, 谢峰. 具有不连续系数的三阶半线性奇异摄动边值问题[J]. 华东师范大学学报(自然科学版), 2017, 2017(2): 20-28.

XUE Hu, XIE Feng. Singularly perturbed third-order semilinear boundary value problems with discontinuous coefficients[J]. Journal of East China Normal University(Natural Sc, 2017, 2017(2): 20-28.

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具有不连续系数的三阶半线性奇异摄动边值问题

Singularly perturbed third-order semilinear boundary value problems with discontinuous coefficients

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