TY - JOUR
T1 - Lyapunov-type inequalities for fractional partial differential equations
AU - Jleli, Mohamed
AU - Kirane, Mokhtar
AU - Samet, Bessem
N1 - Funding Information:
The third author would like to extend his sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the International Research Group Project No. IRG14-04 .
Publisher Copyright:
© 2016 Elsevier Ltd
PY - 2017/4/1
Y1 - 2017/4/1
N2 - We present Lyapunov inequalities for the fractional p-Laplacian (−Δp)s, 1<;p<∞, s∈(0,1), in an open bounded set Ω⊂RN, under homogeneous Dirichlet boundary conditions. We discuss two cases, the case sp>N and the case sp>N. We use the obtained inequalities to provide lower bounds for the first eigenvalue of the fractional p-Laplacian. To the best of our knowledge, this is the first work dealing with Lyapunov-type inequalities for fractional partial differential equations.
AB - We present Lyapunov inequalities for the fractional p-Laplacian (−Δp)s, 1<;p<∞, s∈(0,1), in an open bounded set Ω⊂RN, under homogeneous Dirichlet boundary conditions. We discuss two cases, the case sp>N and the case sp>N. We use the obtained inequalities to provide lower bounds for the first eigenvalue of the fractional p-Laplacian. To the best of our knowledge, this is the first work dealing with Lyapunov-type inequalities for fractional partial differential equations.
KW - Eigenvalues
KW - Fractional p-Laplacian
KW - Fractional Sobolev spaces
KW - Lyapunov inequality
UR - http://www.scopus.com/inward/record.url?scp=85001907721&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2016.10.013
DO - 10.1016/j.aml.2016.10.013
M3 - Article
AN - SCOPUS:85001907721
SN - 0893-9659
VL - 66
SP - 30
EP - 39
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
ER -