Abstract and Applied Analysis

Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p-Laplacian Operator

Jinhua Wang and Hongjun Xiang

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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 .

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 971824, 12 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620772

Digital Object Identifier
doi:10.1155/2010/971824

Mathematical Reviews number (MathSciNet)
MR2720032

Zentralblatt MATH identifier
1209.34005

Citation

Wang, Jinhua; Xiang, Hongjun. Upper and Lower Solutions Method for a Class of Singular Fractional Boundary Value Problems with p -Laplacian Operator. Abstr. Appl. Anal. 2010 (2010), Article ID 971824, 12 pages. doi:10.1155/2010/971824. https://projecteuclid.org/euclid.aaa/1288620772


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