On Semilocal Klein-Gordon-Maxwell Equations
J. Korean Math. Soc.
Published online November 27, 2020
Jongmin Han, Juhee Sohn, and Yeong Seok Yoo
Kyung Hee University, Kookmin 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
MSC numbers : 35J50, 35J61, 81T13
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