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

作     者：陈玉娟 魏雷 张贻民 Yujuan CHEN;Lei WEI;Yimin ZHANG

作者机构：School of ScienceNantong UniversityNantong 226007China School of Mathematics and StatisticsJiangsu Normal UniversityXuzhou 221116China Center for Mathematical SciencesWuhan University of TechnologyWuhan 430070China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2022年第42卷第5期

页      面：2149-2164页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：p-Lapacian Hardy potential symmetry uniqueness asymptotic behavior 

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),p1,θ−p,and T is a half-space{x_(1)0}.When λΘ(where Θ is the Hardy constant),we show that under suitable conditions on f andθ,the equation has a unique positive ***,the exact behavior of the unique positive solution as x_(1)→0^(+),and the symmetric property of the positive solution are obtained.