The European Physical Journal Special Topics

, Volume 222, Issue 8, pp 1999–2013 | Cite as

Infinitely many solutions for a perturbed nonlinear fractional boundary value problems depending on two parameters

  • N. NyamoradiEmail author
  • Y. Zhou
Regular Article


In this paper we prove the existence and multiplicity of (weak) solutions for the following fractional boundary value problem:
where \(\alpha \in (\tfrac{1} {2},1]\), 0 D t α−1 and t D T α−1 are the left and right Riemann-Liouville fractional integrals of order 1 − α respectively, λ,μ ∈ [0,+∞), T > 0, F,GC([0,T] × R N ;R)\{0} and A = (a ij (t)) N×N is symmetric. Our approach is based on variational methods.


European Physical Journal Special Topic Fractional Derivative Fractional Calculus Singular Integral Operator Fractional Boundary 
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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesRazi UniversityKermanshahIran
  2. 2.School of Mathematics and Computational ScienceXiangtan UniversityHunanPR China

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