期刊
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
卷 72, 期 6, 页码 -出版社
SPRINGER INT PUBL AG
DOI: 10.1007/s00033-021-01617-4
关键词
Choquard equation; Hardy-Littlewood-Sobolev inequality; Weighted Sobolev embedding; Trudinger-Moser inequality; Riesz Potential
资金
- CNPq/Brasil [2019/2014]
- Paraiba State Research Foundation (FAPESQ)
In this paper, a class of planar Choquard equation with Riesz potential of logarithm type and decaying potential V and weights K, Q to zero at infinity is investigated. Weighted Sobolev embedding and Trudinger-Moser type inequality are proved using a convenient decomposition. These results address the existence of solutions to the Choquard equation with nonlinearities possessing critical exponential growth in the Trudinger-Moser sense via variational methods.
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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