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

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.

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.