The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications

We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D0+αu(t)+f(t,u(t))+e(t)=0,0<t<1,u(0)=u'(0)=⋯=u(n-2)(0)=0,u(1)=βu(η), where n-1<α≤n,n≥3,0<β≤1,0≤η≤1, D0+α is the standard Riemann-Liouville derivative. Here our n...

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Bibliographic Details
Main Authors: Fuquan Jiang, Xiaojie Xu, Zhongwei Cao
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/531038
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Summary:We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D0+αu(t)+f(t,u(t))+e(t)=0,0<t<1,u(0)=u'(0)=⋯=u(n-2)(0)=0,u(1)=βu(η), where n-1<α≤n,n≥3,0<β≤1,0≤η≤1, D0+α is the standard Riemann-Liouville derivative. Here our nonlinearity f may be singular at u=0. As applications of Green’s function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem.
ISSN:1085-3375
1687-0409