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

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.

     

    Abstract: The Guo-Krasnoselskii's fixed point theorem, the Schauder fixed point theorem and the properties of the associated Green's function are used to study the existence of positive solutions to the coupled system of a class of nonlinear Riemann-Liouville fractional differential equations. Two theorems about the existence of positive solutions are obtained, and two examples are given to illustrate the advantages of the theorems.

     

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