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2012 Multiple Solutions for a Class of Fractional Boundary Value Problems
Ge Bin
Abstr. Appl. Anal. 2012(SI11): 1-16 (2012). DOI: 10.1155/2012/468980


We study the multiplicity of solutions for the following fractional boundary value problem: (d/dt)((1/2)0Dt-β(u'(t))+(1/2)0DT-β(u'(t)))+λF(t,u(t))=0, a.e. t[0,T], u(0)=u(T)=0, where 0Dt-β and 0DT-β are the left and right Riemann-Liouville fractional integrals of order 0β<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.


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Ge Bin. "Multiple Solutions for a Class of Fractional Boundary Value Problems." Abstr. Appl. Anal. 2012 (SI11) 1 - 16, 2012.


Published: 2012
First available in Project Euclid: 4 April 2013

zbMATH: 1253.34009
MathSciNet: MR2991017
Digital Object Identifier: 10.1155/2012/468980

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI11 • 2012
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