| 一类分数阶微分方程边值问题正解的存在性 |
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| 引用本文： | 邹序焱,谢润.一类分数阶微分方程边值问题正解的存在性[J].宁夏大学学报(自然科学版),2014(2):113-116. |
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| 作者姓名： | 邹序焱 谢润 |
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| 作者单位： | 宜宾学院数学研究所,四川宜宾644007 |
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| 基金项目： | 国家自然科学基金资助项目（61370203）;四川省教育厅青年基金资助项目（08ZB002）;宜宾学院科研基金资助项目（2011Q25） |
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| 摘 要： | 研究了一类分数阶微分方程的边值问题:{Dα0+u(t)+f(u(t))=0,u(0)=0,u(1)=0,其中α(1α2)是实数,Dα0+是标准的Riemann-Liouville微分,f:0,+∞)→0,+∞)连续,t∈0,1].利用范数形式的锥拉伸与锥压缩不动点定理,在满足适当的条件下,证明了该边值问题正解的存在性.
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| 关 键 词： | 分数阶微分方程 边值问题 锥拉伸与锥压缩不动点定理 |
Existence of Positive Solutions for Boundary Value Problems with Fraction Differential Equation |
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| Zou Xuyan,Xie Run.Existence of Positive Solutions for Boundary Value Problems with Fraction Differential Equation[J].Journal of Ningxia University(Natural Science Edition),2014(2):113-116. |
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| Authors: | Zou Xuyan Xie Run |
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| Institution: | ( Institute of Mathematics, Yibin University, Yibin 644007, China) |
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| Abstract: | A class of fractional differential equation boundary value problem is studied. {D°0＋u（t）＋f（u（t））=0,u（0）=0,u（1）=0where a （ 1 （ a （ 2 ） is a real number, and D°0＋ is the standard Riemann-Liouville differentiation,t∈0.1] t E E0,1-], and f：O,＋00）→0,＋00） is continuous. By using fixed-point theorem of cone expansion and compression of norm type, the existence of positive solutions for fraction differential equation boundary value problems is proved. |
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| Keywords: | fraction differential equation boundary value problems cone expansion and compression fixedpoint theorem |
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