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arXiv · 2307.15655

Schr\"odinger-Maxwell equations driven by mixed local-nonlocal operators

Nicolò Cangiotti·Maicol Caponi·Alberto Maione·Enzo Vitillaro
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Abstract

In this paper we prove existence of solutions to Schr\"odinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schr\"odinger-Maxwell equations and Schr\"odinger-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.

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Nicolò Cangiotti, Maicol Caponi, Alberto Maione, Enzo Vitillaro. 2023-07-28. Schr\"odinger-Maxwell equations driven by mixed local-nonlocal operators. https://doi.org/10.1007/s13540-024-00251-x

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