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分数阶微分方程多点边值问题的正解 被引量：9

Positive Solutions for Multiple-Point Boundary Value Problem of Fractional Differential Equations
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摘要 研究分数阶微分方程多点边值问题正解的存在性,利用动点定理,得到了边值问题至少存在1个正解和3个正解的充分条件. This paper deals with the existence of positive solutions for multiple-point boundary value problem of fractional differential equations.In light of fixed-point theorems,some sufficient conditions are obtained to guarantee the existence of at least one or three positive solutions of the boundary value problems.
作者 钟文勇
机构地区 吉首大学数学与计算机科学学院
出处 《吉首大学学报（自然科学版）》 CAS 2010年第1期9-12,共4页 Journal of Jishou University(Natural Sciences Edition)
基金 湖南省自然科学基金资助项目(09JJ6010)
关键词 分数阶微分方程 多点边值问题 正解 不动点 fractional differential equations multi-point boundary value problem positive solutions fixed-point theorem
分类号 O175.8 [理学—基础数学]
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参考文献6

  • 1PODLUBNYI.Fractional Differential Equations,Mathematics in Science and Engineering[]..1999
  • 2BAI Z.On Positive Solutions of a Nonlocal Fractional Boundary Value Problem[].Nonlinear Analysis.2010
  • 3SALEM H A H.On the Fractionalm-Point Boundary Value Problemin Reflexive Banach Space and the Weak Topolo-gies[].Journal of Computational and Applied Mathematics.2009
  • 4Leggett R W,Williams L R.Multiple positive fixed points of nonlinear operators on ordered Banach spaces[].Indiana University Mathematics Journal.1979
  • 5Bai,Z. B.,Lü,H. S.Positive solutions for boundary value problem of nonlinear fractional differential equation[].Journal of Mathematical Analysis and Applications.2005
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同被引文献77

  • 1LiHongyu,SunJingxian.POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEM FOR A SYSTEM OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS[J].Annals of Differential Equations,2005,21(2):153-160. 被引量：19
  • 2郭大钧,孙经先.抽象空间微分方程[M].济南:山东科学技术出版社,1989.1～110
  • 3Killbas A A, Srivastava H M,Trujillo J J. Theory and Application of Fraction Differential Equation [M]. North-Holland Mathematic Studies 204.Amsterdam.. Elsevier Science B V, 2006.
  • 4Oldham K B, Spanier J.The Fractional Calculus[M]. New York, London: Academic Press,1974.
  • 5Tatom F B. The relationship between fraction calculus and fractals [J]. Fractals, 1995, 3: 217-229.
  • 6Samko S G , Kilbas A A, Marichev O I. Fractional Integral and Derivatives(Theorey and Applica- tiona) [M]. Switzerland: Gordon and Breach, 1993.
  • 7Zhangbing Bai, Haishen Lu. Positive solution for boundary value problem of nonlinear fractional differential equation [J]. J Math Anal Appl, 2005(311): 495-505.
  • 8E1-Shahed M .Positive solutions for boundary value problems of nonlinear fractional differential equation [M]. Abs Appl Anal 2007. Article ID 10368.
  • 9S. Zhang, Positive solution for boundary value problem of nonlinear fractional differential equations, Elect [J]. Elect Diff Eqns, 2006: 1-12.
  • 10Chuanzhi Bai, Triple positive solutions for a boundary value problem of nonlinear fractional dif- ferential equation [J]. Electronic Journal of Qualitative Theory of Differential Equations 2008, 24: 1-10.

引证文献9

二级引证文献26

吉首大学学报（自然科学版）
2010年 第1期

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