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一类非线性分数阶微分方程耦合系统正解的存在性

薛益民 彭钟琪

薛益民, 彭钟琪. 一类非线性分数阶微分方程耦合系统正解的存在性[J]. 华南师范大学学报(自然科学版), 2020, 52(2): 102-106. doi: 10.6054/j.jscnun.2020032
引用本文: 薛益民, 彭钟琪. 一类非线性分数阶微分方程耦合系统正解的存在性[J]. 华南师范大学学报(自然科学版), 2020, 52(2): 102-106. doi: 10.6054/j.jscnun.2020032
XUE Yimin, PENG Zhongqi. On the Existence of Positive Solutions to the Coupled System of a Class of Nonlinear Fractional Differential Equations[J]. Journal of South China normal University (Natural Science Edition), 2020, 52(2): 102-106. doi: 10.6054/j.jscnun.2020032
Citation: XUE Yimin, PENG Zhongqi. On the Existence of Positive Solutions to the Coupled System of a Class of Nonlinear Fractional Differential Equations[J]. Journal of South China normal University (Natural Science Edition), 2020, 52(2): 102-106. doi: 10.6054/j.jscnun.2020032

一类非线性分数阶微分方程耦合系统正解的存在性

doi: 10.6054/j.jscnun.2020032
基金项目: 

国家自然科学基金项目 11526177

江苏省自然科学基金项目 BK20151160

徐州工程学院培育项目 XKY2017113

详细信息
    通讯作者:

    薛益民,副教授,Email:xueym@xzit.edu.cn

  • 中图分类号: O211.6

On the Existence of Positive Solutions to the Coupled System of a Class of Nonlinear Fractional Differential Equations

  • 摘要: 利用Guo-Krasnoselskii不动点定理、Schauder不动点定理和格林函数的性质,研究一类非线性Riemann-Liouville型分数阶微分方程耦合系统正解的存在性,得到了该耦合系统正解的存在性定理,并举例说明了定理的有效性.
  • [1] SUN Y P, ZHAO M. Positive solutions for a class of fractional differential equations with integral boundary conditions[J]. Applied Mathematics Letters, 2014, 34:17-21. doi: 10.1016/j.aml.2014.03.008
    [2] ZHANG X Q, WANG L, SUN Q. Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter[J]. Applied Mathematics and Computation, 2014, 226:708-718. doi: 10.1016/j.amc.2013.10.089
    [3] CHEN T Y, LIU W B, HU Z G. A boundary value pro-blem for fractional differential equation with P-Laplacian operator at resonance[J]. Nonlinear Analysis, 2012, 75(6):3210-3217. doi: 10.1016/j.na.2011.12.020
    [4] GOODRICH C S. On a fractional boundary value problem with fractional boundary conditions[J]. Applied Mathematics Letters, 2012, 25(8):1101-1105. doi: 10.1016/j.aml.2011.11.028
    [5] GRAEF J R, KONG L J. Positive solutions for a class of higher order boundary value problems with fractional Q-derivatives[J]. Applied Mathematics and Computation, 2012, 218(19):9682-9689. doi: 10.1016/j.amc.2012.03.006
    [6] SHAH K, KHAN R A. Existence and uniqueness of positive solutions to a coupled system of nonlinear fractional order differential equations with anti-periodic boundary conditions[J]. Differential Equations & Applications, 2015, 7(2):245-262.
    [7] JIANG W H. Solvability for a coupled system of fractional differential equations with integral boundary conditions at resonance[J]. Advances in Differential Equations, 2013, 324:1-13. doi: 10.1186/1687-1847-2013-324
    [8] AHMAD B, NTOUYAS S K. A fully Hadamard type integral boundary value problem of a coupled system of fractional differential equations[J]. Fractional Calculus and Applied Analysis, 2014, 17(2):348-360. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=47f19bd98d1cc43baee8c8424dcbe7a8
    [9] SHAH K, KHALIL H, KHAN R A. Upper and lower solutions to a coupled system of nonlinear fractional differential equations[J]. Progress in Fractional Differentiation and Applications, 2016, 2(1):1-10. doi: 10.18576/pfda/020101
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    [12] GUO D J, LAKSHMIKANTHAM V. Nonlinear problems in abstract cones[M]. San Diego:Academic Press, 1988.
    [13] GRANAS A, DUGUNDJI J. Fixed point theory[M]. New York:Springer, 2005.
    [14] 薛益民, 戴振祥, 刘洁.一类Riemann-Liouville型分数阶微分方程正解的存在性[J].华南师范大学学报(自然科学版), 2019, 51(2):105-109. doi: 10.6054/j.jscnun.2019033

    XUE Y M, DAI Z X, LIU J. On the existence of positive solutions to a type of Riemann-Liouville fractional diffe-rential equations[J]. Journal of South China Normal University(Natural Science Edition), 2019, 51(2):105-109. doi: 10.6054/j.jscnun.2019033
    [15] 薛益民, 苏有慧, 刘洁, 等.一类分数阶微分方程耦合系统边值问题解的存在性[J].徐州工程学院学报(自然科学版), 2018, 33(1):41-47.

    XUE Y M, SU Y H, LIU J, et al. Existence of solutions of the boundary value problem to a coupled system of a certain fractional differential equations[J]. Journal of Xuzhou Institute of Technology(Natural Science Edition), 2018, 33(1):41-47.
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出版历程
  • 收稿日期:  2019-07-09
  • 刊出日期:  2020-04-25

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