English

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

Analysis of PDEs 2024-05-01 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2307.15655,
  title  = {Schr\"odinger-Maxwell equations driven by mixed local-nonlocal operators},
  author = {Nicolò Cangiotti and Maicol Caponi and Alberto Maione and Enzo Vitillaro},
  journal= {arXiv preprint arXiv:2307.15655},
  year   = {2024}
}

Comments

arXiv admin note: text overlap with arXiv:2303.11663

R2 v1 2026-06-28T11:43:00.828Z