广西科学2016，Vol.23Issue(4)：374-377,4.DOI:10.13656/j.cnki.gxkx.20160913.002
一类Caputo分数阶微分方程边值问题多解的存在性
Existence of Multiple Solutions for a Caputo Fractional Difference Equation Boundary Value Problem
摘要
Abstract
We investigate the existence and multiplicity of positive solutions for nonlinear Caputo fractional differential equation boundary value problem Dα0+u(t)+f(t,u(t))=0,t∈(0,1),u′(0)=u(1)=0{ , Where 1 <α≤2,f:[0,+∞)× →[0,+∞)is continuous,and Dα0+is the standard Caputo differentiation.In the process of proof,we first transform it into integral equation,then differ-ential equation boundary value problem is further converted to discuss the problem of integral operator fixed point.Finally,by means of Leggett-Williams fixed point theorems on cone,ex-istence results of at least three positive solutions are obtained.The properties of the Green function and the conditions of the nonlinear term is very important.关键词
分数阶微分方程/边值问题/Leggett-Williams不动点定理Key words
fractional difference equation/boundary value problem/Leggett-Williams fixed point theorems分类
数理科学引用本文复制引用
郭彩霞,任玉岗,郭建敏..一类Caputo分数阶微分方程边值问题多解的存在性[J].广西科学,2016,23(4):374-377,4.基金项目
国家自然科学基金项目（No．11271235），大同大学青年科研基金项目（2014Q10）和河南省高等学校重点科研计划项目（15A110047）资助。 （）
