Nonlinear scalar field equation with competing nonlocal terms

被引：5
|
作者：
D'Avenia, Pietro [1 ]
Mederski, Jaroslaw [2 ,3 ]
Pomponio, Alessio [1 ]
机构：
[1] Politecn Bari, Dipartimento Meccan Matemat & Management, Via Orabona 4, I-70125 Bari, Italy
[2] Polish Acad Sci, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw, Poland
[3] Karlsruhe Inst Technol KIT, Dept Math, Inst Anal, D-76128 Karlsruhe, Germany
来源：
NONLINEARITY | 2021年 / 34卷 / 08期
关键词：
elliptic equation; nonlocal problem; Riesz potential; Choquard equation; Hartree equation; mountain pass; NONRADIAL SOLUTIONS; EXISTENCE; SOLITONS; INEQUALITIES;
D O I：
10.1088/1361-6544/ac0d47
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We find radial and nonradial solutions to the following nonlocal problem -Delta u + omega u = (I-alpha* F(u)f(u) - (I-beta*G(u)g(u) in R-N under general assumptions, in the spirit of Berestycki and Lions, imposed on f and g, where N >= 3, 0 <= beta <= alpha <= N, omega >= 0, f,g:R -> R F, G, and I (alpha) , I (beta) are the Riesz potentials. If beta > 0, then we deal with two competing nonlocal terms modelling attractive and repulsive interaction potentials.
引用
收藏
页码：5687 / 5707
页数：21
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