一类无穷区间上分数阶边值问题正解的存在性  

Existence of Positive Solutions for Fractional Boundary Value Problems on the Infinite Interval

作　　者：廖秀 韦煜明 LIAO Xiu;WEI Yuming(Institute of Information Technology,Guilin University of Electronic Technology,Guilin 541004,China;Department of Mathematics and Statistics,Guangxi Normal University,Guilin 541006,China)

机构地区：[1]桂林电子科技大学信息科技学院,桂林541004 [2]广西师范大学数学与统计学院,桂林541006

出　　处：《应用泛函分析学报》2018年第3期258-268,共11页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11361010);广西自然科学基金(2014GXNSFAA118002);2017广西研究生教育创新计划项目(YCSW2017080)

摘　　要：本文主要研究一类无穷区间上分数阶边值问题的正解.通过构造特殊的Banach空间,运用Leray-Schauder非线性抉择得到了该边值问题至少存在一个正解以及运用Leggett-Williams不动点定理得到至少存在三个正解.This paper mainly studies the positive solutions for a class of fractional boundary value problems on infinite intervals. By constructing a special Banach space, we use Leray-Schauder nonlinear choice and Leggett-Wflliams fixed point theorems respectively to obtain the existence of the boundary value problem that it has at least one positive solutions and at least three positive solutions.

关 键 词：分数阶微分方程 无穷区间 边值问题 不动点定理 正解 

分 类 号：O175.1[理学—数学]