| 一类奇异边值问题正解的存在性及多解性 |
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| 引用本文： | 闫东明.一类奇异边值问题正解的存在性及多解性[J].浙江大学学报(理学版),2017,44(3):281. |
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| 作者姓名： | 闫东明 |
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| 作者单位： | 浙江财经大学 数据科学学院, 浙江 杭州 310018 |
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| 基金项目： | 浙江省教育厅一般项目（Y201534471）. |
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| 摘 要： | 应用Dancer全局分歧理论,研究奇异边值问题{u″(t)+a(t)u′(t)+b(t)u(t)+f(t,u(t))=0,t∈(0,1),u(0)=u(1)=0正解的存在性和多解性,其中f:0,1]×0,∞)→0,∞)连续.给出了关于此类问题正解存在的充分条件,该充分条件与相应线性问题的第1个特征值有关,且所涉及的值是最优的.
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| 关 键 词： | 奇异边值问题 全局分歧 正解 多解性 第1特征值 |
| 收稿时间： | 2015-01-04 |
Existence of single and multiple positive solutions of singular boundary value problem |
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| YAN Dongming.Existence of single and multiple positive solutions of singular boundary value problem[J].Journal of Zhejiang University(Sciences Edition),2017,44(3):281. |
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| Authors: | YAN Dongming |
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| Institution: | School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, China |
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| Abstract: | By using Dancer's global bifurcation theorem, we studied the existence of single and multiple positive solutions of the singular boundary value problem .jpg) And the optimal sufficient conditions for the existence of single and multiple positive solutions of the mentioned problem are obtained, which is relate to the first eigenvalue of the relevant linear problem. |
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| Keywords: | singular boundary value problem global bifurcation positive solutions multiple positive solutions first eigenvalue |
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