分数阶常微分方程多点边值问题的上下解方法

Lower and upper solution method for fractional multiple-point boundary value problem

本文应用上下解方法研究了如下分数阶常微分方程多点边值问题{x^((δ))(t)=f(t,x(t)),t∈[a,b],a>0,x(a)+m∑k=1a_kx(t_k)=c解的存在性,其中f:[a,b]×R→R是L^1-Carathéodory函数,δ∈(0,1],c∈R,t_k(k=1,2,…,m)为满足a<t_1<t_2<…<t_m<b,a_k<0以及1+m∑k=1a_k>0的常数.

In this paper, by applying the upper and lower solution method, we study existence of solution for the following fractional multiple-point boundary value problem {x^（δ）（t）=f（t,x（t））,t∈[a,b],a〉0, x（a）＋∑k=1^m akx（tk）=c where f：[a,b]×R→R is L^1-Caratheodory function,δ∈（0,1],c∈R,tk（k=1,2,…,m） are constants and satisfying a〈t1〈t2〈…〈tm〈b,ak〈0,1＋∑k=1^m ak〉0.