| 奇异超线性方程周期边值问题多重正解的存在性 |
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| 引用本文： | 张丽娟,蒋达清,田颖辉.奇异超线性方程周期边值问题多重正解的存在性[J].吉林大学学报(理学版),2009,47(3):487-491. |
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| 作者姓名： | 张丽娟 蒋达清 田颖辉 |
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| 作者单位： | 1. 白城师范学院 数学系, 吉林 白城 137000； 2. 东北师范大学 数学与统计学院, 长春 130024；3. 阜新高等专科学校 数学系, 辽宁 阜新 123000 |
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| 摘 要： | 研究具有奇异超线性周期边值问题多重正解的存在性, 利用非线性Leray Schauder抉择定理和Krasnoselskii锥不动点定理, 证明了在一定条件下, 且非线性项具有奇异和超线性时, 此问题至少存在两个正解.
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| 关 键 词： | 周期边值问题 奇异超线性方程 周期解 Leray Schauder抉择定理 Krasnoselskii锥不动点定理 |
| 收稿时间： | 2008-07-22 |
Existence of Multiplicity of Positive Solutions to Singular Superlinear Equations with Periodic Boundary Value Problems |
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| ZHANG Li-juan,JIANG Da-qing,TIAN Ying-hui.Existence of Multiplicity of Positive Solutions to Singular Superlinear Equations with Periodic Boundary Value Problems[J].Journal of Jilin University: Sci Ed,2009,47(3):487-491. |
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| Authors: | ZHANG Li-juan JIANG Da-qing TIAN Ying-hui |
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| Institution: | 1. Department of Mathematics, Baicheng Normal College, Baicheng 137000, Jilin Province, China；2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China；3. Department of Mathematics, Fuxin Level Specialty College, Fuxin 123000, Liaoning Province, China |
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| Abstract: | This paper deals with the multiplicity of positive solutions to singular superlinear equations with periodic boundary value problems.It is proved that such a problem has at least two positive solutions under our reasonable conditions when the nonlinear term possesses singularity and super-linearity.The proof relies on a nonlinear alternative of Leray-Schauder theorem and Krasnoselskii on fixed point theorem in cones. |
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| Keywords: | periodic boundary value problem singular superlinear equation periodic solution Learay-Schauder alternative theorem Krasnoselskii fixed point theorem in cones |
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