奇异扰动(k, n-k)共轭边值问题的正解

数学物理学报 ›› 2011, Vol. 31 ›› Issue (1): 263-272.

• 论文 • 上一篇

奇异扰动(k, n-k)共轭边值问题的正解

钟敏玲¹|张新光²

1.广东外语外贸大学信息科学技术学院广州 510006|2.烟台大学数学与信息科学学院山东烟台 264005

收稿日期:2009-10-08 修回日期:2010-09-06 出版日期:2011-02-25 发布日期:2011-02-25
基金资助:
国家自然科学基金(10771117)资助

Positive Solutions of Singularly Perturbed (k, n-k) Conjugate Boundary Value Problems

ZHONG Min-Ling¹, ZHANG Xin-Guang²

1.School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006|2.College of Mathematics and Informational Sciences, |Yantai University, Shandong Yantai 264005

Received:2009-10-08 Revised:2010-09-06 Online:2011-02-25 Published:2011-02-25
Supported by:
国家自然科学基金(10771117)资助

摘要/Abstract

摘要：

该文通过构造修正函数, 得到了一类奇异扰动(k, n-k)共轭边值问题多个正解的存在性, 其中, 扰动项仅要求是Lebesgue可积的. 最后给出一个例子说明主要结果的应用.

关键词: 共轭边值问题, 奇异扰动问题, 正解, 修正函数, 不动点指数, 锥

Abstract:

In this paper, by employing the so-called modified function, some new existence results of multiple positive solutions for a class of singularly perturbed (k, n-k) conjugate boundary value problems are established, where the perturbed term is only a Lebesgue integrable function. An example is worked out to indicate the application of the main results.

Key words: Conjugate boundary value problems, Singularly perturbed problem, Positive solutions, Modified function, Fixed point index, Cone

中图分类号:

34B15

钟敏玲, 张新光. 奇异扰动(k, n-k)共轭边值问题的正解[J]. 数学物理学报, 2011, 31(1): 263-272.

ZHONG Min-Ling, ZHANG Xin-Guang. Positive Solutions of Singularly Perturbed (k, n-k) Conjugate Boundary Value Problems[J]. Acta mathematica scientia,Series A, 2011, 31(1): 263-272.

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奇异扰动(k, n-k)共轭边值问题的正解

Positive Solutions of Singularly Perturbed (k, n-k) Conjugate Boundary Value Problems

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