On a planar Choquard equation involving exponential critical growth

被引：0
|
作者：
J. Carvalho
E. Medeiros
B. Ribeiro
机构：
[1] Universidade Federal da Paraíba,Departamento de Matemática
来源：
Zeitschrift für angewandte Mathematik und Physik | 2021年 / 72卷
关键词：
Choquard equation; Hardy-Littlewood-Sobolev inequality; Weighted Sobolev embedding; Trudinger-Moser inequality; Riesz Potential; 35J66; 35J20; 35J60; 35B33;
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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.
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