TY - JOUR
A2 - Yan, Chao
AU - Zhong, Yansheng
PY - 2014
DA - 2014/07/20
TI - A Concentration Phenomenon for p-Laplacian Equation
SP - 148902
VL - 2014
AB - It is proved that if the bounded function of coefficient Qn in the following equation -div {|∇u|p-2∇u}+V(x)|u|p-2u=Qn(x)|u|q-2u, u(x)=0 as x∈∂Ω. u(x)⟶0 as |x|⟶∞ is positive in a region contained in Ω and negative outside the region, the sets {Qn>0} shrink to a point x0∈Ω as n→∞, and then the sequence un generated by the nontrivial solution of the same equation, corresponding to Qn, will concentrate at x0 with respect to W01,p(Ω) and certain Ls(Ω)-norms. In addition, if the sets {Qn>0} shrink to finite points, the corresponding ground states {un} only concentrate at one of these points. These conclusions extend the results proved in the work of Ackermann and Szulkin (2013) for case p=2.
SN - 1110-757X
UR - https://doi.org/10.1155/2014/148902
DO - 10.1155/2014/148902
JF - Journal of Applied Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -