EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS

被引：2
|
作者：
Luo, Yuanyuan [1 ]
Gao, Dongmei [1 ]
Wang, Jun [1 ]
机构：
[1] Jiangsu Univ, Inst Appl Syst Anal, Zhenjiang 212013, Jiangsu, Peoples R China
来源：
ACTA MATHEMATICA SCIENTIA | 2023年 / 43卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Choquard equation; ground state solution; critical points; variational methods; CONCENTRATION-COMPACTNESS PRINCIPLE; SCHRODINGER-EQUATIONS; UNIQUENESS; CALCULUS; DECAY;
D O I：
10.1007/s10473-023-0117-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the Choquard equation -Delta u + V(x)u = b(x) integral(R3) vertical bar u(y)vertical bar(2)/vertical bar x - y vertical bar dyu, x is an element of R-3, where V(x) = V-1(x), b(x) = b(1)(x) for x(1) > 0 and V(x) = V-2(x), b(x) = b(2)(x) for x(1) < 0, and V-1, V-2, b(1) and b(2) are periodic in each coordinate direction. Under some suitable assumptions, we prove the existence of a ground state solution of the equation. Additionally, we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.
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页码：303 / 323
页数：21
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