Limit profiles and uniqueness of ground states to the nonlinear Choquard equations

被引：37

作者：

Seok, Jinmyoung ^{[1
]}

机构：

[1] Kyonggi Univ, Dept Math, 154-42 Gwanggyosan Ro, Suwon 16227, South Korea

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2019年 / 8卷 / 01期

关键词：

Semilinear elliptic; Choquard; limit profile; uniqueness; EXISTENCE;

D O I：

10.1515/anona-2017-0182

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider nonlinear Choquard equations { -Delta u + u = (I-alpha * vertical bar u vertical bar(p))vertical bar u vertical bar(p-2)u in R-N, lim(x)(->infinity) U(x) =0, where I-alpha denotes the Riesz potential and alpha is an element of (0, N). In this paper, we investigate limit profiles of ground states of nonlinear Choquard equations as alpha -> 0 or alpha -> N. This leads to the uniqueness and nondegeneracy of ground states when alpha is sufficiently close to 0 or close to N.

引用

页码：1083 / 1098

页数：16

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