Abstract and Applied Analysis

Multiple Solutions for a Class of Fractional Boundary Value Problems

Ge Bin

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Abstract

We study the multiplicity of solutions for the following fractional boundary value problem: (d / d t) (( 1 / 2) 0 D t - β ( u ' ( t ) ) + (1 / 2) 0 D T - β ( u ' ( t ) ) ) + λ F ( t , u ( t ) ) = 0 ,    a.e.    t [ 0 , T ] ,    u ( 0 ) = u ( T ) = 0 , where 0 D t - β and 0 D T - β are the left and right Riemann-Liouville fractional integrals of order 0 β < 1 , respectively, λ > 0 is a real number, F : [ 0 , T ] × N is a given function, and F ( t , x ) is the gradient of F at x . The approach used in this paper is the variational method. More precisely, the Weierstrass theorem and mountain pass theorem are used to prove the existence of at least two nontrivial solutions.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 468980, 16 pages.

Dates
First available in Project Euclid: 4 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365099930

Digital Object Identifier
doi:10.1155/2012/468980

Mathematical Reviews number (MathSciNet)
MR2991017

Zentralblatt MATH identifier
1253.34009

Citation

Bin, Ge. Multiple Solutions for a Class of Fractional Boundary Value Problems. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 468980, 16 pages. doi:10.1155/2012/468980. https://projecteuclid.org/euclid.aaa/1365099930


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