一类分数阶差分方程边值问题多重正解的存在性

研究一类带有分数阶边界条件的分数阶差分方程多重正解的存在性.分析该方程的Green函数的性质,引入上、下解的概念,并利用Guo-Krasnosel'skii不动点定理和上、下解的方法,分别建立该方程存在正解的充分条件,最后利用Legget-Williams不动点定理,讨论该方程多重正解的存在性.

Existence of multiple positive solutions to a class of fractional difference equations boundary value problems

In this paper,we study the existence of multiple positive solutions for a class of the fractional difference equations with fractional boundary conditions.This paper analyzes some characteristics of the Green’s function,and introduces the concepts of the upper and lower solutions.By Guo-Krasnosel’skii fixed point theorem and the upper and lower solution method,we obtain sufficient conditions for the existence of positive solutions to this equation.Lastly we discuss the existence of multiple positive solutions to this equation by using Legget-Williams fixed point theorem.