期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 355, 期 -, 页码 219-247出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2023.01.023
关键词
MSC: 35R1135B33; 35B38; 47H11; 58E30; 81Q05
类别
In this paper, we investigate the existence and multiplicity of positive bound solutions to the fractional Choquard equation with a positive potential bounded from below. By combining variational methods and the Brouwer degree theory, we obtain extended and improved results in the case where the coefficient V(x) vanishes at infinity.
We deal with the following fractional Choquard equation [GRAPHICS] . where I-mu(x) is the Riesz potential, s is an element of (0, 1), 2s< N not equal 4s, 0 < mu < min{N, 4s} and 2* mu,s= 2N- mu/N-2s is the fractional critical Hardy-Littlewood-Sobolev exponent. By combining variational methods and the Brouwer degree theory, we investigate the existence and multiplicity of positive bound solutions to this equation when V(x) is a positive potential bounded from below. The results obtained in this paper extend and improve some recent works in the case where the coefficient V(x) vanishes at infinity. (c) 2023 Elsevier Inc. All rights reserved.
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