Abstract and Applied Analysis

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

Fuquan Jiang, Xiaojie Xu, and Zhongwei Cao

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Abstract

We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D 0 + α u ( t ) + f ( t , u ( t ) ) + e ( t ) = 0 , 0 < t < 1 , u ( 0 ) = u ' ( 0 ) = = u ( n - 2 ) ( 0 ) = 0 , u ( 1 ) = β u ( η ) , where n - 1 < α n , n 3,0 < β 1,0 η 1 , D 0 + 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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 531038, 12 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450200

Digital Object Identifier
doi:10.1155/2013/531038

Mathematical Reviews number (MathSciNet)
MR3034993

Zentralblatt MATH identifier
1274.34062

Citation

Jiang, Fuquan; Xu, Xiaojie; Cao, Zhongwei. The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 531038, 12 pages. doi:10.1155/2013/531038. https://projecteuclid.org/euclid.aaa/1393450200


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