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Original Articles

Positive properties of Green's function for three-point boundary value problems of nonlinear fractional differential equations and its applications

, , , &
Pages 323-343 | Received 30 Aug 2011, Accepted 02 Sep 2011, Published online: 14 Nov 2011
 

Abstract

In this article, we consider the properties of Green's function for the nonlinear fractional differential equation boundary value problem

where 1 < α < 2, 0 < β, η < 1, is the standard Riemann–Liouville derivative. Here our nonlinearity f may be singular at u = 0. As an application of Green's function, we establish some multiple positive solutions for singular positone and semipositone boundary value problems by means of the Leray–Schauder nonlinear alternative, a fixed-point theorem on cones, and also we give uniqueness of a solution for a singular problem by a mixed monotone method.

AMS Subject Classification:

Acknowledgements

This study was supported by NSFC of China (No. 10971021), the Ministry of Education of China (No. 109051) the Ph.D. Programs Foundation of Ministry of China (No. 200918).

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