Existence of multiple positive solutions for singular boundary value problems of nonlinear fractional differential equations

被引：0
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作者：
Wen-Xue Zhou
Jian-Gang Zhang
Jie-Mei Li
机构：
[1] Lanzhou Jiaotong University,Department of Mathematics
[2] Fudan University,School of Mathematical Sciences
来源：
Advances in Difference Equations | / 2014卷
关键词：
boundary value problem; fractional differential equations; Riemann-Liouville fractional derivative; positive solution; fixed-point theorem;
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摘要：
In this paper, we consider the properties of the Green’s function for the nonlinear fractional differential equation boundary value problem D0+qu(t)=f(t,u(t)), t∈J:=[0,1], u(0)=u′(1)=0, where 1<q≤2 is a real number, and D0+q is the standard Riemann-Liouville differentiation. As an application of the Green’s function, we give some multiple positive solutions for singular boundary value problems, and we also give the uniqueness of solution for a singular problem by means of the Leray-Schauder nonlinear alternative, a fixed-point theorem on cones, and a mixed monotone method.
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