{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:25:42Z","timestamp":1760059542711,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T00:00:00Z","timestamp":1750377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Capes, CNPq, FAPDF Edital","award":["04\/2021","2022\/16407-1","2022\/16097-2","P2022YFAJH","CUP E5324001950001"],"award-info":[{"award-number":["04\/2021","2022\/16407-1","2022\/16097-2","P2022YFAJH","CUP E5324001950001"]}]},{"DOI":"10.13039\/501100001807","name":"Fapesp","doi-asserted-by":"publisher","award":["04\/2021","2022\/16407-1","2022\/16097-2","P2022YFAJH","CUP E5324001950001"],"award-info":[{"award-number":["04\/2021","2022\/16407-1","2022\/16097-2","P2022YFAJH","CUP E5324001950001"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]},{"name":"PRIN PNRR","award":["04\/2021","2022\/16407-1","2022\/16097-2","P2022YFAJH","CUP E5324001950001"],"award-info":[{"award-number":["04\/2021","2022\/16407-1","2022\/16097-2","P2022YFAJH","CUP E5324001950001"]}]},{"name":"INdAM\u2014GNAMPA Project","award":["04\/2021","2022\/16407-1","2022\/16097-2","P2022YFAJH","CUP E5324001950001"],"award-info":[{"award-number":["04\/2021","2022\/16407-1","2022\/16097-2","P2022YFAJH","CUP E5324001950001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper we discuss some results on the existence of solutions for an elliptic system appearing in physical sciences. In particular the system appears when we look at standing wave solutions in the electrostatic situation for the Schr\u00f6dinger equation coupled, with the minimal coupling rule, with the electromagnetic equations of Born\u2013Infeld theory. Many difficulties appear, especially due to the fact we are in an unbounded domain (the whole space R3) and to the intrinsic nonlinear nature of the equations. We are able to prove the existence of a minimal energy solution by showing an approximating procedure that can be adapted depending on the value of the parameter p, which is in the nonlinearity.<\/jats:p>","DOI":"10.3390\/axioms14070481","type":"journal-article","created":{"date-parts":[[2025,6,20]],"date-time":"2025-06-20T06:50:45Z","timestamp":1750402245000},"page":"481","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ground State for a Schr\u00f6dinger\u2013Born\u2013Infeld System via an Approximating Procedure"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5823-0392","authenticated-orcid":false,"given":"Gaetano","family":"Siciliano","sequence":"first","affiliation":[{"name":"Department of Mathematics, Universit\u00e0 degli Studi di Bari Aldo Moro, Via E. Orabona 4, 70125 Bari, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/s00574-018-0111-y","article-title":"On the Schr\u00f6dinger-Born-Infeld System","volume":"50","author":"Azzollini","year":"2018","journal-title":"Bull. Braz. Math. Soc. New Ser."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"125326","DOI":"10.1016\/j.jmaa.2021.125326","article-title":"A perturbation approach for the Schr\u00f6dinger-Born-Infeld system: Solutions in the subcritical and critical case","volume":"503","author":"Liu","year":"2021","journal-title":"J. Math. Anal. 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