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

被引：1

作者：

Chen, Yujuan ^{[1
]}

Wei, Lei ^{[2
]}

Zhang, Yimin ^{[3
]}

机构：

[1] Nantong Univ, Sch Sci, Nantong 226007, Peoples R China

[2] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

[3] Wuhan Univ Technol, Ctr Math Sci, Wuhan 430070, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2022年 / 42卷 / 05期

关键词：

p-Lapacian; Hardy potential; symmetry; uniqueness; asymptotic behavior; SEMILINEAR ELLIPTIC-EQUATIONS; BLOW-UP SOLUTIONS; MAXIMUM;

D O I：

10.1007/s10473-022-0524-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study a nonlinear equation in the half-space with a Hardy potential, specifically, -Delta(p)u = lambda u(p-1)/x(1)(p) - x(1)(theta) f(u) in T, where Delta(p) stands for the p-Laplacian operator defined by Delta(p)u = div(vertical bar del u vertical bar(p-2)del u), p > 1, theta > -p, and T is a half-space {x(1) > 0}. When lambda > Theta (where Theta is the Hardy constant), we show that under suitable conditions on f and theta, 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.

引用

页码：2149 / 2164

页数：16

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