Asymptotic Behavior of Least Energy Solutions for a Fractional Laplacian Eigenvalue Problem on R^(N)  

作　　者：Yun Bo WANG Xiao Yu ZENG Huan Song ZHOU 

机构地区：[1]School of Mathematics and Center for Nonlinear Studies,Northwest University,Xi'an 710127,P.R.China [2]Center for Mathematical Sciences,Wuhan University of Technology,Wuhan 430070,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第4期707-727,共21页数学学报（英文版）

基　　金：Supported by NSFC (Grant Nos.11931012,11871387,11871395 and 12171379)。

摘　　要：We are interested in the existence and asymptotic behavior for the least energy solutions of the following fractional eigenvalue problem (P)(-△)^(s)u+V(x)u=μu+am(x)|u|^(4s/N)u,∫_(R^(N))|u|^(2)dx=1,u∈H^(s)(R^(N)),where s∈(0,1),μ∈R,a>0,V(x)and m(x)are L^(∞)(R^(N))functions with N≥2.We prove that there is a threshold a^(*)_(s)>0 such that problem(P)has a least energy solution u_(a)(x)for each a∈(0,a^(*)_(s))and u_(a)blows up,as a↗a^(*)_(s),at some point x_(0)∈R^(N),which makes V(x_(0))be the minimum and m(x_(0))be the maximum.Moreover,the precise blowup rates for u_(a)are obtained under suitable conditions on V(x)and m(x).

关 键 词：LAPLACIAN eigenvalue problem constrained variational problem energ mates 

分 类 号：O177[理学—数学]