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On semilocal Klein-Gordon-Maxwell equations

손주희|유영석|한종민
대한수학회 (The Korean Mathematical Society)|2021.09|대한수학회지 (Journal of the KMS)|제58권 제5호|pp. 1131-1145|DOI 10.4134/JKMS.j200463

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키워드

Semilocal gauge field modelKlein-Gordon-Maxwell equationsmountain pass solutionsPohozaev identity
주제분류수학

초록

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 $p=6$.

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 $p=6$.

참고문헌 (18)

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