摘要
In this article,we study the following critical problem involving the fractional Laplacian:{(−Δ)^α/2u−γu/|x|^α=λ|u|^q−2/|x|^s+|u|^2^∗α^(t)−2u/|x|^t in Ω,u=0 in R^N∖Ω,whereΩ⊂R^N(N>α)is a bounded smooth domain containing the origin,α∈(0,2),0≤s,t<α,1≤q<2,λ>0,2α^*(t)=2(N-t)/N-αis the fractional critical Sobolev-Hardy exponent,0≤γ<γH,and γH is the sharp constant of the Sobolev-Hardy inequality.We deal with the existence of multiple solutions for the above problem by means of variational methods and analytic techniques.
作者
Jinguo ZHANG
Tsing-San HSU
张金国;许清山(School of Mathematics,Jiangxi Normal University,Nanchang 330022,China;Center for General Education,Chang Gung University,Tao-Yuan,Taiwan,China)
