分数阶p-Laplacian耦合系统边值问题正解的存在性

The Existence of Positive Solutions for the Fractional Order Coupled System with P-Laplacian Operator

讨论了一类带有p-Laplacian算子的分数阶微分方程耦合系统边值问题正解的存在性,通过Green函数将微分系统转化为等价的积分系统,应用Banach压缩映像原理,Leray-Schauder非线性抉择和锥拉伸定理等证明耦合系统正解的存在性,并给出了应用实例.

In this paper, we discuss the existence of positive solutions for the boundary value problem of coupled system of fractional differential equations with p-Laplacian operator. By using the Green function, the differential system is transformed into an equivalent integral system. We prove the existence of positive solutions by using Banach contraction mapping principle, Leray-Schauder fixed point theorem and Guo-Krasnosel＇ skii fixed point theorem on cones. Finally, two examples are provided to illustrate our main results.