Schrödinger-Maxwell equations driven by mixed local-nonlocal operators

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.

arXiv commentarXiv admin note: text overlap with arXiv:2303.11663

References in corpus (5)

• Fractional Schrodinger equation
• Ground state solutions to the nonlinear Schrodinger-Maxwell equations
• Ground state solutions for nonlinear fractional Schrödinger equations in ${\mathbb{R}}^N$
• Variational methods for nonpositive mixed local-nonlocal operators
• Klein-Gordon-Maxwell equations driven by mixed local-nonlocal operators