Journal of the
Korean Mathematical Society
JKMS

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

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J. Korean Math. Soc. 2021; 58(5): 1131-1145

Online first article November 27, 2020      Printed September 1, 2021

https://doi.org/10.4134/JKMS.j200463

Copyright © The Korean Mathematical Society.

On semilocal Klein-Gordon-Maxwell equations

Jongmin Han, Juhee Sohn, Yeong Seok Yoo

Kyung Hee University; Kookmin University; Kyung Hee University

Abstract

In this article, we study the Klein-Gordon-Maxwell equations arising from a semilocal gauge field model. This model describes the interaction of two complex scalar fields and one gauge field, and generalizes the classical Klein-Gordon equation coupled with the Maxwell electrodynamics. We prove that there exist infinitely many standing wave solutions for $p\in (2,6)$ which are radially symmetric. Here, $p$ comes from the exponent of the potential of scalar fields. We also prove the nonexistence of nontrivial solutions for the critical case $p=6$.

Keywords: Semilocal gauge field model, Klein-Gordon-Maxwell equations, mountain pass solutions, Pohozaev identity

MSC numbers: Primary 35J50, 35J61, 81T13

Supported by: Jongmin Han was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2018 R1D1A1B07042681).

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