| 非线性分数阶微分方程特征值问题正解的存在性 |
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| 引用本文： | 代群,刘素莉,李辉来. 非线性分数阶微分方程特征值问题正解的存在性[J]. 吉林大学学报(理学版), 2015, 53(1): 1-4 |
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| 作者姓名： | 代群 刘素莉 李辉来 |
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| 作者单位： | 1. 长春理工大学 理学院, 长春 130022； 2. 吉林大学 数学学院, 长春 130012 |
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| 摘 要： | 应用拉伸压缩不动点定理研究非线性分数阶微分方程特征值问题的正解,得到了正解的存在性.结果表明,对于一类α阶非线性分数阶微分方程的特征值问题(3α≤4),当特征值参数满足在一给定开区间时,该微分方程至少存在一个正解.
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| 关 键 词： | 分数阶微分方程 正解 特征值问题 不动点定理 |
| 收稿时间： | 2014-05-21 |
Existence of Positive Solutions for Nonlinear Fractional Eigenvalue Problem |
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| DAI Qun,LIU Suli,LI Huilai. Existence of Positive Solutions for Nonlinear Fractional Eigenvalue Problem[J]. Journal of Jilin University: Sci Ed, 2015, 53(1): 1-4 |
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| Authors: | DAI Qun LIU Suli LI Huilai |
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| Affiliation: | 1. School of Science, Changchun University of Science and Technology, Changchun 130022, China;2. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | We used the fixed point theorem of cone expansion and cone compression to study the eigenvalue problem of nonlinear fractional differential equation so as to obtain the existence of positive solutions. The results show that for a type of α order fractional differential equation eigenvalue problem (3<α≤4), the differential equation has at least one positive solution when eigenvalue parameter belongs to an open interval. |
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| Keywords: | fractional differential equation positive solution eigenvalue problem fixed point theorem |
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