一类分数阶微分方程边值问题的Lyapunov不等式及其正解的存在性

Lyapunov Inequality and Existence of Positive Solutions for Boundary Value Problems of a Class of Fractional Differential Equations

本文研究含Hadamard分数阶导数的分数阶微分方程边值问题.通过对Green函数性质的讨论,得到其对应的Lyapunov-type不等式和Lyapunov不等式,同时利用Guo-Krasnoselskii不动点定理证明了一类非线性边值问题正解的存在性.

In this paper, boundary value problems of fractional differential equations with Hadamard fractional derivatives are studied. By discussing the properties of Green’s function,the corresponding Lyapunov-type inequality and Lyapunov inequality are obtained. At the same time, the existence of positive solutions for a class of nonlinear boundary value problems is proved by using Guo-Krasnoselskii fixed point theorem.