Multiple Solutions for a Class of Fractional Boundary Value Problems | Zendy

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Multiple Solutions for a Class of Fractional Boundary Value Problems

Author(s) -

Bin Ge

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/468980

Subject(s) - mathematics , combinatorics , multiplicity (mathematics) , matrix (chemical analysis) , value (mathematics) , path (computing) , mathematical analysis , statistics , chemistry , computer science , chromatography , programming language

We study the multiplicity of solutions for the following fractional boundary value problem: where and are the left and right Riemann-Liouville fractional integrals of order , respectively, is a real number, is a given function, and is the gradient of at . 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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