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.
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页码：440 / 455
页数：16
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