Abstract and Applied Analysis

Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity

Yongqing Wang, Lishan Liu, and Yonghong Wu

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Abstract

We discuss the existence of positive solutions to the following fractional m-point boundary value problem with changing sign nonlinearity D 0 + α u ( t ) + λ f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = 0 , D 0 + β u ( 1 ) = i = 1 m - 2 η i D 0 + β u ( ξ i ) , where λ is a positive parameter, 1 < α 2 , 0 < β < α - 1 , 0 < ξ 1 < < ξ m - 2 < 1 with i = 1 m - 2 η i ξ i α - β - 1 < 1 , D 0 + α is the standard Riemann-Liouville derivative, f and may be singular at t = 0 and/or t = 1 and also may change sign. The work improves and generalizes some previous results.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 214042, 17 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168373

Digital Object Identifier
doi:10.1155/2012/214042

Mathematical Reviews number (MathSciNet)
MR2955012

Zentralblatt MATH identifier
1247.35192

Citation

Wang, Yongqing; Liu, Lishan; Wu, Yonghong. Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 214042, 17 pages. doi:10.1155/2012/214042. https://projecteuclid.org/euclid.aaa/1365168373


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