一类非线性分数阶微分方程多重正解存在的充分条件

Sufficient conditions for the existence of multiple positive solutions of a class of nonlinear fractional differential equations

研究了一类非线性分数阶微分方程边值问题的多重正解存在性.首先分析了方程格林函数的性质,然后利用Guo-Krasnosel’skii不动点定理得到了当系数μ(t)满足不同条件时,该边值问题至少存在1个正解和至少存在2个正解的充分条件.

The existence of multiple positive solutions for a class of boundary value problems of nonlinear fractional differential equations is studied.Firstly,the properties of the Green’s function of the equation are analyzed,and then the sufficient conditions for the existence of at least one positive solution and at least two positive solutions of the boundary value problem are obtained by using Guo-Krasnosel’skii fixed point theorem when the coefficientμ(t)satisfies different conditions.