Nonlinear Choquard equations: Doubly critical case

被引：39

作者：

Seok, Jinmyoung ^{[1
]}

机构：

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

来源：

APPLIED MATHEMATICS LETTERS | 2018年 / 76卷

关键词：

Semilinear elliptic; Choquard equation; Critical exponent; Variational method; EXISTENCE;

D O I：

10.1016/j.aml.2017.08.016

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*F(u))F'(u) in R-N lim u (x) = 0, x ->infinity where I-alpha denotes Riesz potential and alpha is an element of (0, N). In this paper, we show that when F is doubly critical, i.e. F(u) = N/N+alpha vertical bar u vertical bar(N+alpha/N) + N-2/N+alpha vertical bar u vertical bar (N + alpha/N -2) , the nonlinear Choquard equation admits a nontrivial solution if N >= 5 and alpha + 4 < N. (c) 2017 Elsevier Ltd. All rights reserved.

引用

页码：148 / 156

页数：9

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