Abstract and Applied Analysis

Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem

Chuanzhi Bai

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Abstract

This paper is concerned with the existence of three solutions to a nonlinear fractional boundary value problem as follows: ( d / d t ) ( ( 1 / 2 ) 0 D t α - 1 ( 0 C D t α u ( t ) ) - ( 1 / 2 ) t D T α - 1 ( t C D T α u ( t ) ) ) + λ a ( t ) f ( u ( t ) ) = 0 , a . e .    t [ 0 , T ] , u ( 0 ) = u ( T ) = 0 , where α ( 1 / 2,1 ] , and λ is a positive real parameter. The approach is based on a critical-points theorem established by G. Bonanno.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 963105, 13 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168351

Digital Object Identifier
doi:10.1155/2012/963105

Mathematical Reviews number (MathSciNet)
MR2969986

Zentralblatt MATH identifier
1253.34008

Citation

Bai, Chuanzhi. Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 963105, 13 pages. doi:10.1155/2012/963105. https://projecteuclid.org/euclid.aaa/1365168351


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