Entire Sign-Changing Solutions to the Fractional Critical Schrodinger Equation  

作　　者：Xingdong Tang Guixiang Xu Chunyan Zhang Jihui Zhang 

机构地区：[1]School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing,Jiangsu 210044,China [2]Laboratory of Mathematics and Complex Systems(Ministry of)Education),School of Mathematical Sciences,Beijing Normal University,Beijing 100875,China [3]School of Mathematical Sciences,Nanjing Normal University,Nanjing,Jiangsu 210046,China

出　　处：《Annals of Applied Mathematics》2024年第3期219-248,共30页应用数学年刊（英文版）

基　　金：supported by National Key Research and Development Program of China(No.2020YFA0712900);NSFC(No.112371240 and No.12431008);supported by NSFC(No.12001284)。

摘　　要：In this paper,we consider the fractional critical Schrödinger equation(FCSE)(-Δ)^(s)u-|u|2^(*)s-2 u=0,where u∈˙H^(s)(R^(N)),N≥4,0<s<1 and 2^(*)s=2 N/N-2 s is the critical Sobolev exponent of order s.By virtue of the variational method and the concentration compactness principle with the equivariant group action,we obtain some new type of nonradial,sign-changing solutions of(FCSE)in the energy space˙H^(s)(R^(N)).The key component is that we take the equivariant group action to construct several subspace of˙H^(s)(R^(N))with trivial intersection,then combine the concentration compactness argument in the Sobolev space with fractional order to show the compactness property of Palais-Smale sequences in each subspace and obtain the multiple solutions of(FCSE)in˙H^(s)(R^(N)).

关 键 词：Fractional critical Schrodinger equation sign-changing solution the concentration-compactness principle the equivariant group action the mountain pass theorem 

分 类 号：O175[理学—数学]