Published Paper

Inserted: 22 mar 2023
Last Updated: 6 nov 2023

Journal: Milan Journal of Mathematics
Volume: 91
Number: 2
Pages: 375-403
Year: 2023
Doi: 10.1007/s00032-023-00387-0

Abstract:

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.

Keywords: Variational methods, Nonlocal operators, Fractional Operators, Critical points theory, Klein–Gordon–Maxwell system