广西师范大学学报(自然科学版)2017,Vol.35Issue(4):68-75,8.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
Existence of Positive Solutions for a Class of Two-point Boundary Value Problem of Fractional Differential Equations
摘要
Abstract
In this paper,a class of two-point boundary value problem of fractional differential equations are studied:Dα0+u(t)=-f(t,u(t)), 0<t<1,u(0)=u′(0)=u′(1)=0,{ where 2 <α≤ 3,Dα0+ 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.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Key words
fractional differential equation/Banach 's contraction principle/cohesive mapping/fixed point index分类
数理科学引用本文复制引用
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):68-75,8.基金项目
国家自然科学基金(11361010) (11361010)
广西自然科学基金(2014GXNSFAA118002) (2014GXNSFAA118002)
广西研究生教育创新计划(YCSW2017080) (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 ()