Multiple Solutions for a Class of Fractional Boundary Value Problems
Author
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-10-24
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
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)))+λ∇F(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 0≤β<1, respectively, λ>0 is a real number, F:[0,T]×ℝN→ℝ 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.
American Psychological Association (APA)
Bin, Ge. 2012. Multiple Solutions for a Class of Fractional Boundary Value Problems. Abstract and Applied Analysis،Vol. 2012, no. 2012, pp.1-16.
https://search.emarefa.net/detail/BIM-473930
Modern Language Association (MLA)
Bin, Ge. Multiple Solutions for a Class of Fractional Boundary Value Problems. Abstract and Applied Analysis No. 2012 (2012), pp.1-16.
https://search.emarefa.net/detail/BIM-473930
American Medical Association (AMA)
Bin, Ge. Multiple Solutions for a Class of Fractional Boundary Value Problems. Abstract and Applied Analysis. 2012. Vol. 2012, no. 2012, pp.1-16.
https://search.emarefa.net/detail/BIM-473930
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473930