Calculus of Variations and Geometric Measure Theory

N. Cangiotti - M. Caponi - A. Maione - E. Vitillaro

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

created by maione on 22 Mar 2023



Inserted: 22 mar 2023

Year: 2023

ArXiv: 2303.11663 PDF


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.