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一类非线性分数阶微分方程边值问题的正解 被引量：1

Positive Solution to Boundary Value Problem for a Class of Nonlinear Fractional Differential Equation
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摘要 利用锥拉伸和压缩不动点定理研究一类非线性分数阶微分方程积分边值问题,获得了其相应的格林函数及正解的存在性条件,并给出了应用实例. Using fixed point theory of cone expansion and compression of norm type,we investigated a class of boundary value problem for nonlinear fractional differential equation with integral conditions.The relevant Green function and some sufficient conditions on the existence of positive solutions were established.Some examples were given to illustrate the application of the result.
作者 李耀红
机构地区 宿州学院数学与统计学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2015年第1期21-26,共6页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:11226119) 安徽省高校自然科学基金重点项目(批准号:KJ2014A252)
关键词 正解 积分边值问题 分数阶微分方程 不动点定理 positive solution integral boundary value problem fractional differential equation fixed point theory
分类号 O175.8 [理学—基础数学]
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参考文献10

  • 1YAO Qingliu. Positive Solutions for Eigenvalue Problems of Fourth-Order Elastic Beam Equations EJ]. Appl Math Lett, 2004, 17(2): 237-243.
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二级参考文献12

  • 1Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations [M]. Amsterdam: Elsevier, 2006.
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  • 6YANG Xiong, WEI Zhong-li, WEI Dong. Existence of Positive Solutions for the Boundary Value Problem of Nonlinear Fractional Differential Equations[J]. Commun Nonlinear Sci Numer Simul, 2012, 17(1) : 85-92.
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  • 8Ahmada Bashir, Nieto J J. Existence Results for a Coupled System of Nonlinear Fractional Differential Equations with Three-Point Boundary Conditions [J]. Comput Math Appl, 2009, 58(9): 1838-1843.
  • 9ZHAO Yi-ge, SUN Shu-rong, HAN Zhen-lai, et al. Positive Solutions for a Coupled System of Nonlinear Differential Equations of Mixed Fractional Orders [J]. Advances in Difference Equations, 2011, 2011(1) : 64-69.
  • 10JIANG Wei-hua. Solvability for a Coupled System of Fractional Differential Equations at Resonance [J]. Nonlinear Anal, 2012, 13(5): 2285-2292.

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吉林大学学报（理学版）
2015年 第1期

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