On a planar Choquard equation involving exponential critical growth

被引：6

作者：

Carvalho, J. ^{[1
]}

Medeiros, E. ^{[1
]}

Ribeiro, B. ^{[1
]}

机构：

[1] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2021年 / 72卷 / 06期

关键词：

Choquard equation; Hardy-Littlewood-Sobolev inequality; Weighted Sobolev embedding; Trudinger-Moser inequality; Riesz Potential; NONLINEAR SCHRODINGER-EQUATIONS; GROUND-STATE SOLUTIONS; EXISTENCE;

D O I：

10.1007/s00033-021-01617-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a class of planar Choquard equation with Riesz potential of logarithm type and the potential V and the weights K, Q decaying to zero at infinity. We prove a weighted Sobolev embedding and a weighted Trudinger-Moser type inequality using a convenient decomposition. These results allow us to address, via variational methods, the existence of solutions to the Choquard equation when the nonlinearities possess critical exponential growth in the Trudinger-Moser sense.

引用

页数：19

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