Eur. Phys. J. Special Topics 222, 1999-2013 (2013)
https://doi.org/10.1140/epjst/e2013-01980-2

Regular Article

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

¹ Department of Mathematics, Faculty of Sciences, Razi University, 67149 Kermanshah, Iran
² School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, PR China

^a e-mail: nyamoradi@razi.ac.ir; neamat80@yahoo.com
^b e-mail: yzhou@xtu.edu.cn

Received: 3 June 2013
Revised: 6 August 2013
Published online: 7 October 2013

Abstract

In this paper we prove the existence and multiplicity of (weak) solutions for the following fractional boundary value problem: where α ∊ (½,1], ₀D_t^α−1 and _tD_T^α−1 are the left and right Riemann-Liouville fractional integrals of order 1 − α respectively, λ,μ ∊ [0,+∞), T > 0, F,G ∊ C([0,T] × R^N;R)\{0} and A = (a_ij(t))_N×N is symmetric. Our approach is based on variational methods.