带有Riemann-Liouville分数阶导数的边值问题多正解的存在性(英文)

Existence of Multiple Positive Solutions for a Boundary Value Problem with Riemann-Liouville's Fractional Derivative

本文运用Avery-Peterson不动点定理研究以下分数阶边值问题Dα0+Dα0+u=f(t,u,u′,-Dα0+u,-Dα+10+u),t∈[0,1],u(0)=u′(0)=u′(1)=Dα0+u(0)=Dα+10+u(0)=Dα+10+u(1)={0至少三个正解的存在性,其中α∈(2,3]是一实数,Dα0+是α阶Riemann-Liouville分数阶导数.文章最后提供一个具体的例子来说明所得到的结论.

In this work, by virtue of Avery-Peterson fixed point theorem, we are mainly concerned with the existence result of at least triple positive solutions for the fractional boundary value problem {D0^α＋D0^α＋u=f（t,u,u＇,-D0^α＋u,-D0＋^α＋1u）,t∈[0,1],u（0）=u＇（0）=u＇（1）=D0＋^αu（0）=D0＋^α＋1u（0）=D0＋^α＋1u（1）=0 Here α∈ （2,3] is a real number, D0＋^α is the standard Riemann-Liouville fractional derivative of order a. Finally,we offer an example to illustrate Our main result.