Standing Waves of Fractional Schrödinger Equations with Potentials and General Nonlinearities  

作　　者：Zaizheng Li Qidi Zhang Zhitao Zhang 

机构地区：[1]School of Mathematical Sciences,Hebei Normal University,Shijiazhuang,Hebei 050024,China [2]Hebei Center for Applied Mathematics,Shijiazhuang,Hebei 050024,China [3]Department of Mathematics,The University of Hong Kong,Hong Kong,China [4]School of Mathematical Sciences,Jiangsu University,Zhenjiang,Jiangsu 212013,China [5]HLM,Academy of Mathematics and Systems Science,the Chinese Academy of Sciences,Beijing 100190,China [6]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Analysis in Theory and Applications》2023年第4期357-377,共21页分析理论与应用（英文刊）

基　　金：funded by Natural Science Foundation of Hebei Province(No.A2022205007);Science and Technology Project of Hebei Education Department(No.QN2022047);Science Foundation of Hebei Normal University(No.L2021B05);supported by National Natural Science Foundation of China(Nos.11771428,12031015 and 12026217).

摘　　要：We study the existence of standing waves of fractional Schrodinger equations with a potential term and a general nonlinear term:iut-(-Δ)^(s)u-V(x)u+f(u)=0,(t,x)∈R_(+)×R^(N),where s∈(0,1),N>2s is an integer and V(x)≤0 is radial.More precisely,we investigate the minimizing problem with L2-constraint:E(a)=inf{1/2∫_(R_(N))|(-△)^(s/2)u|^(2)+V(x)|u|^(2)-2F(|u|)|u∈H^(s)(R^(N)),||u||_(L^(2))^(2)(R^(N))=α.Under general assumptions on the nonlinearity term f(u)and the potential term V(x),we prove that there exists a constant a00 such that E(a)can be achieved for all a>a_(0),and there is no global minimizer with respect to E(a)for all 0<a<a_(0).Moreover,we propose some criteria determining a0=0 or a_(0)>0.

关 键 词：Fractional Schrodinger equation standing wave normalized solution 

分 类 号：O175.29[理学—数学]