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浙江大学学报（理学版）
浙江大学学报（理学版）  2017, Vol. 44 Issue (3): 281-286,338    DOI: 10.3785/j.issn.1008-9497.2017.03.006
数学与计算机科学     
一类奇异边值问题正解的存在性及多解性
闫东明
浙江财经大学 数据科学学院, 浙江 杭州 310018
Existence of single and multiple positive solutions of singular boundary value problem
YAN Dongming
School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, China
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摘要： 应用Dancer全局分歧理论，研究奇异边值问题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.
关键词： 奇异边值问题;  全局分歧;  正解;  多解性;  第1特征值    
Abstract: By using Dancer's global bifurcation theorem, we studied the existence of single and multiple positive solutions of the singular boundary value problem 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.
Key words: singular boundary value problem    global bifurcation    positive solutions    multiple positive solutions    first eigenvalue
收稿日期: 2015-01-04 出版日期: 2017-03-01
CLC:  O175.8  
基金资助: 浙江省教育厅一般项目（Y201534471）.
作者简介: 闫东明(1982-),ORCID:http://orcid.org/0000-0002-2893-4871,男,博士,讲师,主要从事微分方程研究,E-mail:13547895541@126.com.
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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): 281-286,338.

YAN Dongming. Existence of single and multiple positive solutions of singular boundary value problem. Journal of Zhejiang University (Science Edition), 2017, 44(3): 281-286,338.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.03.006    或    https://www.zjujournals.com/sci/CN/Y2017/V44/I3/281

[1] O' REGAN D. Singular Dirichlet boundary value problems I. Superlinear and nonresonant case [J]. Nonlinear Analysis,1997,29:221-245.
[2] ASAKAWA H. Nonresonant singular two-point boundary value problems [J]. Nonlinear Analysis,2001,44:791-809.
[3] XU X, MA J P. A note on singular nonlinear boundary value problems [J]. J Math Anal Appl,2004,293:108-124.
[4] HAN G D, WU Y. Nontrivial solutions of singular two-point boundary value problems with sign-changing nonlinear terms [J]. J Math Anal Appl,2007,325:1327-1338.
[5] DALMASSO R. Positive solutions of singular boundary value problems [J]. Nonlinear Analysis,1996,27:645-652.
[6] AGARWAL R P, WONG F H, LIAN W C. Positive solutions for nonlinear singular boundary value problems [J]. Appl Math Letters,2002,130(2/3):225-234.
[7] HA K S, LEE Y H. Existence of multiple positive solutions of singular boundary value problems [J]. Nonlinear Analysis,1997,28(8):1429-1438.
[8] LI J M, WANG J X. Triple positive solutions for a type of second-order singular boundary problems [J]. Boundary Value Problems,2010,2010(1):1-14.
[9] MA R Y, THOMPSON B. Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities [J]. J Math Anal Appl,2005,303:726-735.
[10] MA R Y. Global behavior of the components of nodal solutions of asymptotically linear eigenvalue problems [J]. Applied Mathematics Letters,2008,21:754-760.
[11] DANCER E. Global solution branches for positive mappings [J]. Arch Rat Mech Anal,1973,52:181-192.
[12] ZEIDLER E. Nonlinear Functional Analysis and Its Applications, I. Fixed-Point Theorems[M]. New York: Springer-Verlag,1985.
[13] DEIMLING K. Nonlinear Functional Analysis[M]. New York: Springer-Verlag,1985.
[14] GUO D, LAKSHMIKANTHAM V. Nonlinear Problems in Abstract Cones[M]. New York: Academic Press,1988.
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