THE ASYMPTOTIC BEHAVIOR AND SYMMETRY OF POSITIVE SOLUTIONS TO p-LAPLACIAN EQUATIONS IN A HALF-SPACE  

作　　者：Yujuan CHEN Lei WEI Yimin ZHANG 陈玉娟;魏雷;张贻民(School of Science,Nantong University,Nantong 226007,China;School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,China;Center for Mathematical Sciences,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]School of Science,Nantong University,Nantong 226007,China [2]School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,China [3]Center for Mathematical Sciences,Wuhan University of Technology,Wuhan 430070,China

出　　处：《Acta Mathematica Scientia》2022年第5期2149-2164,共16页数学物理学报（B辑英文版）

基　　金：supported by NSFC(11871250);supported by NSFC(11771127,12171379);the Fundamental Research Funds for the Central Universities(WUT:2020IB011,2020IB017,2020IB019).

摘　　要：We study a nonlinear equation in the half-space with a Hardy potential,specifically,−Δ_(p)u=λu^(p−1)x_(1)^(p)−x_(1)^(θ)f(u)in T,where Δp stands for the p-Laplacian operator defined by Δ_(p)u=div(∣Δu∣^(p−2)Δu),p>1,θ>−p,and T is a half-space{x_(1)>0}.When λ>Θ(where Θ is the Hardy constant),we show that under suitable conditions on f andθ,the equation has a unique positive solution.Moreover,the exact behavior of the unique positive solution as x_(1)→0^(+),and the symmetric property of the positive solution are obtained.

关 键 词：p-Lapacian Hardy potential SYMMETRY UNIQUENESS asymptotic behavior 

分 类 号：O175[理学—数学]