Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2021; 58(6): 1327-1345

Online first article September 27, 2021      Printed November 1, 2021

https://doi.org/10.4134/JKMS.j200616

Copyright © The Korean Mathematical Society.

A Liouville theorem of an integral equation of the Chern-Simons-Higgs type

Qinghua Chen, Yayun Li, Mengfan Ma

Nanjing Normal University; Nanjing University of Finance \& Economics; Nanjing Normal University

Abstract

In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation of Chern-Simons-Higgs type \begin{equation*} u(x)=\overrightarrow{l}+C_{*}\int_{\mathbb{R}^n}\frac{(1-|u(y)|^2)|u(y)|^2u(y)-\frac{1}{2}(1-|u(y)|^2)^2u(y)}{|x-y|^{n-\alpha}}dy. \end{equation*} Here $u:\mathbb{R}^n\rightarrow \mathbb{R}^k$ is a bounded, uniformly continuous function with $k\geqslant1$ and $0<\alpha

Keywords: Chern-Simons-Higgs equation, Liouville theorem, Riesz potential, finite energy solution

MSC numbers: 35Q56, 45G05, 45E10

Supported by: This research was supported by National Natural Science Foundation of China (11871278).