TY - JOUR
A2 - Xu, Fuyi
AU - Wu, Wenquan
AU - Zhou, Xiangbing
PY - 2013
DA - 2013/03/25
TI - Eigenvalue of Fractional Differential Equations with -Laplacian Operator
SP - 137890
VL - 2013
AB - We investigate the existence of positive solutions for the fractional order eigenvalue problem with p-Laplacian operator -𝒟tβ(φp(𝒟tαx))(t)=λf(t,x(t)),t∈(0,1),x(0)=0,𝒟tαx(0)=0,𝒟tγx(1)=∑j=1m-2aj𝒟tγx(ξj), where 𝒟tβ,𝒟tα,𝒟tγ are the standard Riemann-Liouville derivatives and p-Laplacian operator is defined as φp(s)=|s|p-2s,p>1.f:(0,1)×(0,+∞)→[0,+∞) is continuous and f can be singular at t=0,1 and x=0. By constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of fractional differential equation is established.
SN - 1026-0226
UR - https://doi.org/10.1155/2013/137890
DO - 10.1155/2013/137890
JF - Discrete Dynamics in Nature and Society
PB - Hindawi Publishing Corporation
KW -
ER -