Multiplicity results for a class of fractional boundary value problems

Nemat Nyamoradi. "Multiplicity results for a class of fractional boundary value problems." Annales Polonici Mathematici 109.1 (2013): 59-73. <http://eudml.org/doc/280907>.

@article{NematNyamoradi2013,
abstract = {We prove the existence of at least three solutions to the following fractional boundary value problem: ⎧ $-d/dt (1/2 _0D_t^\{-σ\} (u^\{\prime \}(t)) + 1/2 _tD_T^\{-σ\} (u^\{\prime \}(t))) - λβ(t)f(u(t)) - μγ(t)g(u(t)) = 0$, a.e. t ∈ [0, T], ⎨ ⎩ u (0) = u (T) = 0, where $_0D_t^\{-σ\}$ and $_tD_T^\{-σ\}$ are the left and right Riemann-Liouville fractional integrals of order 0 ≤ σ < 1 respectively. The approach is based on a recent three critical points theorem of Ricceri [B. Ricceri, A further refinement of a three critical points theorem, Nonlinear Anal. 74 (2011), 7446-7454].},
author = {Nemat Nyamoradi},
journal = {Annales Polonici Mathematici},
keywords = {fractional differential equations; three solutions; Caputo fractional derivative; critical point},
language = {eng},
number = {1},
pages = {59-73},
title = {Multiplicity results for a class of fractional boundary value problems},
url = {http://eudml.org/doc/280907},
volume = {109},
year = {2013},
}

TY - JOUR
AU - Nemat Nyamoradi
TI - Multiplicity results for a class of fractional boundary value problems
JO - Annales Polonici Mathematici
PY - 2013
VL - 109
IS - 1
SP - 59
EP - 73
AB - We prove the existence of at least three solutions to the following fractional boundary value problem: ⎧ $-d/dt (1/2 _0D_t^{-σ} (u^{\prime }(t)) + 1/2 _tD_T^{-σ} (u^{\prime }(t))) - λβ(t)f(u(t)) - μγ(t)g(u(t)) = 0$, a.e. t ∈ [0, T], ⎨ ⎩ u (0) = u (T) = 0, where $_0D_t^{-σ}$ and $_tD_T^{-σ}$ are the left and right Riemann-Liouville fractional integrals of order 0 ≤ σ < 1 respectively. The approach is based on a recent three critical points theorem of Ricceri [B. Ricceri, A further refinement of a three critical points theorem, Nonlinear Anal. 74 (2011), 7446-7454].
LA - eng
KW - fractional differential equations; three solutions; Caputo fractional derivative; critical point
UR - http://eudml.org/doc/280907
ER -