Klein-Gordon-Maxwell equations driven by mixed local-nonlocal operators

Classical results concerning Klein-Gordon-Maxwell type systems are shortly reviewed and generalized to the setting of mixed local-nonlocal operators, where the nonlocal one is allowed to be nonpositive definite according to a real parameter. In this paper, we provide a range of parameter values to e...

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Bibliographic Details
Published in:arXiv.org 2023-07
Main Authors: Cangiotti, Nicolò, Caponi, Maicol, Maione, Alberto, Vitillaro, Enzo
Format: Article
Language:English
Subjects:
Critical point
Maxwell's equations
Operators
Parameters
Online Access:Get full text
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Summary:Classical results concerning Klein-Gordon-Maxwell type systems are shortly reviewed and generalized to the setting of mixed local-nonlocal operators, where the nonlocal one is allowed to be nonpositive definite according to a real parameter. In this paper, we provide a range of parameter values to ensure the existence of solitary (standing) waves, obtained as Mountain Pass critical points for the associated energy functionals in two different settings, by considering two different classes of potentials: constant potentials and continuous, bounded from below, and coercive potentials.
ISSN:2331-8422
DOI:10.48550/arxiv.2303.11663