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

页码：5687 / 5707

页数：21

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