一类分数阶微分方程三点边值问题的多重正解

Existence of multiple positive solution for fractional differential equation three-point boundary value problem

主要研究了一类Riemann-Liouville分数阶微分方程三点边值问题多重正解的存在性,通过格林函数的正性和上下解方法建立了边值问题{D0α+y(t)+f(t,y(t))=0,0<t<1;y(0)=0,y(1)=βy(η)的单一正解的存在性,应用Leray-Schauder非线性抉择定理和Guo-Krasnosel'skii不动点定理得到了该边值问题的多重正解的存在性.

In this paper,the authors studied the existence on multiple positive solutions for the nonlinear fractional differential equation three-point boundary value problem in the Riemann-Liouville sense.By the properties of Green function and lower and upper solution method,the existence of single positive solution for BVP{Dα0＋y（t）＋f（t,y（t））=0,0〈t〈1;y（0）=0,y（1）=βy（η）is established.Furthermore,the existence of multiple positive solutions for the problem is also obtained by using Leray-Schauder nonlinear alternative theorem and Guo-Krasnosel＇skii fixed point theorem.