On the Choquard equation with double critical Sobolev exponents in RN

被引：0

作者：

Liu, Zhongyuan ^{[1
]}

Liu, Ziying ^{[1
]}

Xu, Wenhuan ^{[1
]}

机构：

[1] Henan Univ, Sch Math & Stat, Kaifeng, Peoples R China

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2025年 / 70卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Choquard equation; ground state solution; double critical exponents; NONLINEAR ELLIPTIC PDE; EXISTENCE;

D O I：

10.1080/17476933.2024.2310228

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the existence and nonexistence results to the Choquard equation -Delta u = (integral(RN) vertical bar u(y)vertical bar(2)*(alpha)/vertical bar x - y vertical bar(alpha) dy) vertical bar u vertical bar(2 alpha)*(-2)u +/- vertical bar u vertical bar(q-2)u in R-N, where 2(alpha)* = 2N-alpha/N-2, 0 < alpha < N, 1 < q = 2*, 2* = 2N/N-2, N >= 3. We first use the Pohozaev-type identity to show the nonexistence of solutions for 1 < q < 2*. When the equation has double critical exponents, i.e. q = 2*, we obtain the existence of radial ground state solutions by the Nehari manifold and Mountain pass theorem.

引用

页码：440 / 455

页数：16

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