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2012 Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity
Yongqing Wang, Lishan Liu, Yonghong Wu
Abstr. Appl. Anal. 2012(SI01): 1-17 (2012). DOI: 10.1155/2012/214042

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.

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Yongqing Wang. Lishan Liu. Yonghong Wu. "Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity." Abstr. Appl. Anal. 2012 (SI01) 1 - 17, 2012. https://doi.org/10.1155/2012/214042

Information

Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1247.35192
MathSciNet: MR2955012
Digital Object Identifier: 10.1155/2012/214042

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI01 • 2012
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