TY - JOUR
T1 - A critical Kirchhoff type problem involving a nonlocal operator
AU - Fiscella, Alessio
AU - Valdinoci, Enrico
PY - 2014/1/1
Y1 - 2014/1/1
N2 - In this paper we show the existence of non-negative solutions for a Kirchhoff type problem driven by a nonlocal integrodifferential operator, that is -M(∥-u∥-Z2) LKu=λf(x,u)+| u|2*-2u in Ω,u=0in Rn\-Ω where L K is an integrodifferential operator with kernel K, Ω is a bounded subset of Rn, M and f are continuous functions, ∥̇ ∥Z is a functional norm and 2* is a fractional Sobolev exponent.
AB - In this paper we show the existence of non-negative solutions for a Kirchhoff type problem driven by a nonlocal integrodifferential operator, that is -M(∥-u∥-Z2) LKu=λf(x,u)+| u|2*-2u in Ω,u=0in Rn\-Ω where L K is an integrodifferential operator with kernel K, Ω is a bounded subset of Rn, M and f are continuous functions, ∥̇ ∥Z is a functional norm and 2* is a fractional Sobolev exponent.
KW - Fractional
KW - Kirchhoff equation
KW - Laplacian
KW - Vibrating string
UR - http://www.scopus.com/inward/record.url?scp=84884301124&partnerID=8YFLogxK
U2 - 10.1016/j.na.2013.08.011
DO - 10.1016/j.na.2013.08.011
M3 - Article
VL - 94
SP - 156
EP - 170
JO - Nonlinear Analysis: Theory Methods & Applications
JF - Nonlinear Analysis: Theory Methods & Applications
SN - 0362-546X
ER -