THE RADIAL SYMMETRY OF POSITIVE SOLUTIONS FOR SEMILINEAR PROBLEMS INVOLVING WEIGHTED FRACTIONAL LAPLACIANS  

作　　者：王英 邱妍静 尹青苹 Ying WANG;Yanjing QIU;Qingping YIN(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang,330022,China)

机构地区：[1]School of Mathematics and Statistics,Jiangxi Normal University,Nanchang,330022,China

出　　处：《Acta Mathematica Scientia》2024年第3期1020-1035,共16页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(12001252);the Jiangxi Provincial Natural Science Foundation(20232ACB211001)。

摘　　要：This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)_(γ)~su=b(x)f(u)in B_(1){0},u=h in R~N B_(1),where b:B_1→R is locally Holder continuous,radially symmetric and decreasing in the|x|direction,F:R→R is a Lipschitz function,h:B_1→R is radially symmetric,decreasing with respect to|x|in R^(N)/B_(1),B_(1) is the unit ball centered at the origin,and(-Δ)_γ~s is the weighted fractional Laplacian with s∈(0,1),γ∈[0,2s)defined by(-△)^(s)_(γ)u(x)=CN,slimδ→0+∫R^(N)/B_(δ)(x)u(x)-u(y)/|x-y|N+2s|y|^(r)dy.We consider the radial symmetry of isolated singular positive solutions to the nonlocal problem in whole space(-Δ)_(γ)^(s)u(x)=b(x)f(u)in R^(N)\{0},under suitable additional assumptions on b and f.Our symmetry results are derived by the method of moving planes,where the main difficulty comes from the weighted fractional Laplacian.Our results could be applied to get a sharp asymptotic for semilinear problems with the fractional Hardy operators(-Δ)^(s)u+μ/(|x|^(2s))u=b(x)f(u)in B_(1)\{0},u=h in R^(N)\B_(1),under suitable additional assumptions on b,f and h.

关 键 词：radial symmetry fractional Laplacian method of moving planes 

分 类 号：O177[理学—数学]