{"title":"Schrödinger-Maxwell equations driven by mixed local-nonlocal operators","authors":"","doi":"10.1007/s13540-024-00251-x","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>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.</p>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13540-024-00251-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
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.
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