Semiclassical states for fractional Schrödinger equations with critical growth

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• 作者：Qing Guo ^{guoqing@amss.ac.cn} ; Xiaoming He ; ^{xmhe923@muc.edu.cn}
• 关键词：35J20 ; 35J65
• 刊名：Nonlinear Analysis: Theory, Methods & Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：151
• 期：Complete
• 页码：164-186
• 全文大小：767 K
• 卷排序：151

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.