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分数阶微分方程积分边值问题多个正解的存在性

The Existence of Multiple Positive Solutions of Boundary Value Problem for Fractional Differential Equations with Integral Boundary Conditions
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摘要 研究了带有积分边值条件的分数阶微分方程的边值问题.利用LeggettWilliams不动点定理,以及一些分析技巧得到了这类分数阶微分方程边值问题多个正解的存在性. In this paper we discuss the boundary value problem for fractional differential equations with integral boundary conditions. By using the Leggett-Williams fixed point theorem and some analysis techniques, we obtain the existence of multiple positive solutions of the boundary value problems.
作者 薛云 周宗福
机构地区 安徽大学数学科学学院
出处 《数学的实践与认识》 CSCD 北大核心 2014年第22期275-280,共6页 Mathematics in Practice and Theory
基金 国家自然科学基金(11071001) 安徽省自然科学基金(1208085MA13)
关键词 分数阶 边值问题 正解 fractional order boundary value problems positive solutions
分类号 O175.8 [理学—基础数学]
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参考文献8

  • 1Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equa- tions[M]. North-Holl and Mathematics Studies, Amsterdam: Elsevier, 2006.
  • 2Podlubny I. Factional Differential Equations[M]. New York: Academic Press, 1993.
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  • 5Xu X J, Jiang D (Qa, Yuan C J. Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation[J]. Nonlinear Analysis, 2009(71): 4676-4688.
  • 6华守亮,吕志伟.分数阶微分方程边值问题解的存在性及唯一性[J].河南大学学报（自然科学版）,2010,40(5):453-455. 被引量：6
  • 7章美月,刘文斌.分数阶微分方程积分边值问题解的存在性[J].应用泛函分析学报,2013,15(2):167-171. 被引量：2
  • 8张立新,王海菊.含积分边界条件的分数阶微分方程边值问题的正解的存在性[J].纯粹数学与应用数学,2013,29(5):450-457. 被引量：7

二级参考文献23

  • 1Kilbas A A, Srivastava H M, Trujillo. J.J. Theory and Applications of Fractional Differential Equations[M]// North- Holland Mathematics Studies. Amsterdam: Elsevier, 2006.
  • 2Podlubny. I. Fractional Differential Equations[M]. New York: Academic press, 1993.
  • 3Zhanbing Bai, Haishen I.u, Positive solutions for boundary value problem of nonlinear fractional differential equation[J]. J. Math. Anal. Appl. , 2005(31):1495-505.
  • 4Daqing Jiang, Chengjun Yuan. The positive properties of the Green funtion for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application[J]. Nonlinear Anal. , 2010,72:710-719.
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  • 10Liang Sihua, Zhang Jihui. Positive solutions for boundary value problems of nonlinear fractional differential equation [J]. Nonlinear Anal., 2009,71:5545-5550.

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数学的实践与认识
2014年 第22期

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