一类分数阶微分方程两点边值问题正解的存在性

doi:10.16088/j.issn.1001-6600.2017.04.010

广西师范大学学报（自然科学版） ›› 2017, Vol. 35 ›› Issue (4): 68-75.doi: 10.16088/j.issn.1001-6600.2017.04.010

一类分数阶微分方程两点边值问题正解的存在性

庞杨,韦煜明^*,冯春华

广西师范大学数学与统计学院,广西桂林541006

出版日期:2017-07-25 发布日期:2018-07-25
通讯作者: 韦煜明(1974—), 男, 广西桂平人,广西师范大学教授,博士。E-mail:ymwei@gxnu.edu.cn
基金资助:
国家自然科学基金(11361010);广西自然科学基金(2014GXNSFAA118002);广西研究生教育创新计划(YCSW2017080);广西高等学校高水平创新团队及卓越学者计划;广西高校数学与统计模型重点实验室开放基金

Existence of Positive Solutions for a Class of Two-point BoundaryValue Problem of Fractional Differential Equations

PANG Yang,WEI Yuming^*,FENG Chunhua

College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China

Online:2017-07-25 Published:2018-07-25

摘要/Abstract

摘要： 本文研究一类分数阶微分方程的两点边值问题:D^α₀₊u(t)=-f(t,u(t)), 0α₀₊是标准的Riemann-Liouville微分,f:[0,1]×[0,∞)→[0,∞)是连续函数。本文利用Banach压缩映像原理得到解的唯一性,并在较一般的非紧性测度条件下应用凝聚映射的不动点指数得到该边值问题正解的存在性。

关键词: 分数阶微分方程, 压缩映像原理, 凝聚映射, 不动点指数

Abstract: In this paper, a class of two-point boundary value problem of fractional differential equations are studied:D^α₀₊u(t)=-f(t,u(t)), 0α≤3, D^α₀₊ is the standard Riemann-Liouville fractional derivative. The uniqueness of solution of the fractional two-point boundary value problem is acquired by using Banach’s contraction mapping principle, and the existence of positive solutions for the boundary value problem is obtained by using the fixed point index of the cohesive mapping under the general noncompactness measure condition.

Key words: fractional differential equation, Banach’s contraction principle, cohesive mapping, fixed point index

庞杨,韦煜明,冯春华. 一类分数阶微分方程两点边值问题正解的存在性[J]. 广西师范大学学报（自然科学版）, 2017, 35(4): 68-75.

PANG Yang,WEI Yuming,FENG Chunhua. Existence of Positive Solutions for a Class of Two-point BoundaryValue Problem of Fractional Differential Equations[J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(4): 68-75.

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一类分数阶微分方程两点边值问题正解的存在性

Existence of Positive Solutions for a Class of Two-point BoundaryValue Problem of Fractional Differential Equations

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