一类分数阶m点边值问题正解的存在性

The Existence of Positive Solution for a Kind of Fractional Order m-point Boundary Value Problem

本文利用偏序集上的不动点定理,研究了分数阶m点边值问题Dα0+u(t)+f(t,u(t))=0,0<t<1,α∈(n-1,n],n 2,u(0)=u′(0)=…=u(n-2)(0),u(1)=∑mi=-12βiu(ξi),在一定条件下讨论了该边值问题正解的存在唯一性以及严格递增区间。

In this paper,a kind of fractional order m-point boundary value problem Dα0＋u（t）＋f（t,u（t））=0,0t1,α∈（n-1,n],n≥2,u（0）=u′（0）=…=u（n-2）（0）,u（1）=∑m-2i=1βiu（ξi） is studied with the fixed point theorem of partially ordered sets.Furthermore,the existence and uniqueness of the positive solution of this boundary value problem and its strict increasing interval are discussed under certain conditions.