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2010 Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator
Jinhua Wang, Hongjun Xiang
Abstr. Appl. Anal. 2010: 1-12 (2010). DOI: 10.1155/2010/971824

Abstract

The upper and lower solutions method is used to study the p -Laplacian fractional boundary value problem D 0 + γ ( ϕ p ( D 0 + α u ( t ) ) ) = f ( t , u ( t ) ) , 0 < t < 1 , u ( 0 ) = 0 , u ( 1 ) = a u ( ξ ) , D 0 + α u ( 0 ) = 0 , and D 0 + α u ( 1 ) = b D 0 + α u ( η ) , where 1 < α , γ 2 , 0 a , b 1 , 0 < ξ , η < 1 . Some new results on the existence of at least one positive solution are obtained. It is valuable to point out that the nonlinearity f can be singular at t = 0,1 or u = 0 .

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Jinhua Wang. Hongjun Xiang. "Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator." Abstr. Appl. Anal. 2010 1 - 12, 2010. https://doi.org/10.1155/2010/971824

Information

Published: 2010
First available in Project Euclid: 1 November 2010

zbMATH: 1209.34005
MathSciNet: MR2720032
Digital Object Identifier: 10.1155/2010/971824

Rights: Copyright © 2010 Hindawi

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