Published Paper

Inserted: 31 jul 2023
Last Updated: 27 feb 2024

Journal: Fractional Calculus and Applied Analysis
Year: 2024
Doi: 10.1007/s13540-024-00251-x

Abstract:

In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schrödinger-Maxwell equations and Schrödinger-Maxwell equations with a coercive potential, and the main novelty is that the nonlocal part of the operator is allowed to be nonpositive definite according to a real parameter. We then 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.