Abstract and Applied Analysis

Positive Solutions for Multipoint Boundary Value Problem of Fractional Differential Equations

Wenyong Zhong

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Abstract

We study the existence and multiplicity of positive solutions for the fractional m -point boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ' ( 0 ) = 0 , u ' ( 1 ) = i = 1 m - 2 a i u ' ( ξ i ) , where 2 < α < 3 , D 0 + α is the standard Riemann-Liouville fractional derivative, and f : [ 0 , 1 ] × [ 0 , ) [ 0 , ) is continuous. Here, a i 0 for i = 1 , , m - 2 , 0 < ξ 1 < ξ 2 < < ξ m - 2 < 1 , and ρ = i = 1 m - 2 a i ξ i α - 2 with ρ < 1 . In light of some fixed point theorems, some existence and multiplicity results of positive solutions are obtained.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 601492, 15 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313170935

Digital Object Identifier
doi:10.1155/2010/601492

Mathematical Reviews number (MathSciNet)
MR2746013

Zentralblatt MATH identifier
1223.34008

Citation

Zhong, Wenyong. Positive Solutions for Multipoint Boundary Value Problem of Fractional Differential Equations. Abstr. Appl. Anal. 2010 (2010), Article ID 601492, 15 pages. doi:10.1155/2010/601492. https://projecteuclid.org/euclid.aaa/1313170935


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