[1]薛益民,戴振祥,刘洁.一类分数阶微分方程耦合系统正解的多重性[J].徐州工程学院学报(自然科学版),2020,(03):59-63.
 XUE Yimin,DAI Zhenxiang,LIU Jie.Multiplicity of Positive Solutions to a Coupled System of Fractional Differential Equations[J].Journal of Xuzhou Institute of Technology(Natural Sciences Edition),2020,(03):59-63.
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一类分数阶微分方程耦合系统正解的多重性()
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《徐州工程学院学报》(自然科学版)[ISSN:1674-358X/CN:32-1789/N]

卷:
期数:
2020年03期
页码:
59-63
栏目:
理论研究
出版日期:
2020-09-30

文章信息/Info

Title:
Multiplicity of Positive Solutions to a Coupled System of Fractional Differential Equations
文章编号:
1674-358X(2020)03-0059-05
作者:
薛益民戴振祥刘洁
(徐州工程学院 数学与统计学院,江苏 徐州221018)
Author(s):
XUE YiminDAI ZhenxiangLIU Jie
(School of Mathematics and Statistics,Xuzhou University of Technology,Xuzhou 221018,China)
关键词:
分数阶微分方程 耦合系统 正解 Green函数 不动点定理
Keywords:
fractional differential equations coupled system positive solution Green's function fixed point theorem
分类号:
O175.8
文献标志码:
A
摘要:
运用Guo|Krasnosel'skii's不动点定理和Green函数的性质,研究一类非线性分数阶微分方程耦合系统正解的多重性问题,构造了该耦合系统两个正解存在的充分条件,并证明了所得结论的正确性.
Abstract:
By applying Guo|Krasnosel'skii's fixed point theorem and the properties of Green's function,the multiplicity of positive solutions to a coupled system of nonlinear Riemann|Liouville fractional differential equations were studied,and sufficient conditions for the existence of two positive solutions to the coupled system were established and proved.

参考文献/References:

[1] SUN Y,ZHAO M.Positive solutions for a class of fractional differential equations with integral boundary conditions[J].Applied Mathematics Letters,2014,34(1):17|21.
[2] ZHANG X,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,2014,44(1/2):293|316.
[3] CHEN T,LIU W,HU Z.A boundary value problem for fractional differential equation with P|laplacian operator at resonance[J].Nonlinear Analysis,2012,75(6):3210|3217.
[4] GOODRICH S.On a fractional boundary value problem with fractional boundary conditions[J].Applied Mathematics Letters,2012,25(8):1101|1105.
[5] GRAEF J R,KONG L.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.
[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.Solvability for acoupled system of fractional differential equations with integral boundary conditions at resonance[J].Advances in Differential Equations,2013,324(1):1|13.
[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.
[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.)
[10] JLELI M,SAMET B.Existence of positive solutions to a coupled system of fractional differential equations[J].Mathematical Methods in the Applied Sciences,2015,38(6):1014|1031.
[11] 薛益民,戴振祥.一类非线性Riemann|Liouville分数阶微分方程耦合系统的正解[J].徐州工程学院学报(自然科学版),2019,34(3):64|68.
[12] 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.
[13] XU X J,JIANG D Q,YUAN C J.Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation[J].Nonlinear Analysis,2009,71(10):4676|4688.

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[1]吴彦强.一类分数阶微分方程共振边值问题解的存在性[J].徐州工程学院学报(自然科学版),2016,(2):40.
 WU Yanqiang.Solvability for a Class of Fractional m-Point Boundary Value Problem at Resonance[J].Journal of Xuzhou Institute of Technology(Natural Sciences Edition),2016,(03):40.
[2]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,(1):41.
 XUE Yimin,SU Youhui,LIU Jie,et al.Existence of Solutions of the Boundary Value Problem to a Coupled System of a Certain Fractional Differential Equation[J].Journal of Xuzhou Institute of Technology(Natural Sciences Edition),2018,(03):41.
[3]薛益民,戴振祥.一类非线性Riemann-Liouville分数阶 微分方程耦合系统的正解[J].徐州工程学院学报(自然科学版),2019,(03):64.
 XUE Yimin,DAI Zhenxiang.Positive Solutions to a Coupled System of Nonlinear Riemann-Liouville Fractional Differential Equations[J].Journal of Xuzhou Institute of Technology(Natural Sciences Edition),2019,(03):64.

备注/Memo

备注/Memo:
收稿日期:2020-05-05
基金项目:国家自然科学数学天元基金项目(11526177); 江苏省自然科学基金项目(BK20151160); 徐州工程学院培育项目(XKY2017113)
作者简介:薛益民(1977-),男,副教授,博士研究生,主要从事微分方程及其应用研究.
更新日期/Last Update: 2020-09-30