文摘
In this paper, we consider the following fractional nonlinear Schrödinger equations ε2s(−Δ)su+V(x)u=P(x)g(u)+Q(x)|u|2s∗−2u,x∈RN and prove the existence and concentration of positive solutions under suitable assumptions on the potentials V(x),P(x)V(x),P(x) and Q(x)Q(x). We show that the semiclassical solutions uεuε with maximum points xεxε concentrating at a special set SPSP characterized by V(x),P(x)V(x),P(x) and Q(x)Q(x). Moreover, for any sequence xε→x0∈SPxε→x0∈SP, vε(x):=uε(εx+xε)vε(x):=uε(εx+xε) convergence strongly in Hs(RN)Hs(RN) to a ground state solution vv of (−Δ)sv+V(x0)v=P(x0)g(v)+Q(x0)|v|2s∗−2v,x∈RN.