Positive solutions to the planar logarithmic Choquard equation with exponential nonlinearity

被引：6

作者：

Cassani, Daniele ^{[1
,2
]}

Du, Lele ^{[1
,2
]}

Liu, Zhisu ^{[3
,4
]}

机构：

[1] Univ Insubria, Dipartimento Sci & Alta Tecnol, Como, Italy

[2] RISM Riemann Int Sch Math Villa Toeplitz, Via GB Vico 46, I-21100 Varese, Italy

[3] China Univ Geosci, Ctr Math Sci, Sch Math & Phys, Wuhan 430074, Hubei, Peoples R China

[4] Univ Insubria Villa Toeplitz, Dipartimento Sci & Alta Tecnol, Via GB Vico 46, I-21100 Varese, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2024年 / 241卷

基金：

中国国家自然科学基金;

关键词：

Schrodinger-Poisson systems; Asymptotic analysis; Critical growth; Concentration-compactness principle; Variational method; ELLIPTIC-EQUATIONS; EXISTENCE;

D O I：

10.1016/j.na.2023.113479

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the following nonlinear Choquard equation ( ) -Au + u= ln 1 |x | * F(u) f (u), in R2, where f is an element of C1(R, R) and F is the primitive of the nonlinearity f vanishing at zero. We use an asymptotic approximation approach to establish the existence of positive solutions to the above problem in the standard Sobolev space H1(R2). We give a new proof and at the same time extend part of the results established in (Cassani-Tarsi, Calc.Var.PDE, 2021) [11].

引用

页数：19

共 25 条

[1] Groundstates of the Choquard equations with a sign-changing self-interaction potential [J].