Electron. J. Differential Equations,
Vol. 2016 (2016), No. 306, pp. 111.
Multiplicity of solutions to a nonlocal Choquard equation
involving fractional magnetic operators and critical exponent
Fuliang Wang, Mingqi Xiang
Abstract:
In this article, we study the multiplicity of solutions to a nonlocal
fractional Choquard equation involving an external magnetic potential
and critical exponent, namely,
where
, b>0,
,
,
is a signchanging scalar potential,
is the magnetic potential,
is the fractional magnetic operator,
is a parameter,
is the critical exponent
in the sense of the HardyLittlewoodSobolev inequality and
.
Under suitable assumptions on a,b and
,
we obtain multiplicity
of nontrivial solutions by using variational methods.
In particular, we obtain the existence of infinitely many nontrivial solutions
for the degenerate Kirchhoff case, that is, a=0, b>0.
Submitted October 27, 2016. Published November 30, 2016.
Math Subject Classifications: 49A50, 26A33, 35J60, 47G20.
Key Words: Choquard equation; fractional magnetic operator;
variational method; critical exponent.
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Fuliang Wang
College of Science
Civil Aviation University of China
Tianjin 300300, China
email: flwang@cauc.edu.cn


Mingqi Xiang
College of Science
Civil Aviation University of China
Tianjin 300300, China
email: xiangmingqi_hit@163.com

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