{"id":"https://openalex.org/W4411494722","doi":"https://doi.org/10.3390/axioms14070481","title":"Ground State for a Schr\u00f6dinger\u2013Born\u2013Infeld System via an Approximating Procedure","display_name":"Ground State for a Schr\u00f6dinger\u2013Born\u2013Infeld System via an Approximating Procedure","publication_year":2025,"publication_date":"2025-06-20","ids":{"openalex":"https://openalex.org/W4411494722","doi":"https://doi.org/10.3390/axioms14070481"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14070481","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070481","pdf_url":"https://www.mdpi.com/2075-1680/14/7/481/pdf?version=1750414965","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/7/481/pdf?version=1750414965","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051216000","display_name":"Gaetano Siciliano","orcid":"https://orcid.org/0000-0001-5823-0392"},"institutions":[{"id":"https://openalex.org/I5561750","display_name":"University of Bari Aldo Moro","ror":"https://ror.org/027ynra39","country_code":"IT","type":"education","lineage":["https://openalex.org/I5561750"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Gaetano Siciliano","raw_affiliation_strings":["Department of Mathematics, Universit\u00e0 degli Studi di Bari Aldo Moro, Via E. Orabona 4, 70125 Bari, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Universit\u00e0 degli Studi di Bari Aldo Moro, Via E. Orabona 4, 70125 Bari, Italy","institution_ids":["https://openalex.org/I5561750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051216000"],"corresponding_institution_ids":["https://openalex.org/I5561750"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20077301,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"7","first_page":"481","last_page":"481"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7040935754776001},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5655351877212524},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5104588270187378},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.5066972374916077},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4753163456916809},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.459532767534256},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.4522581100463867},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4500666856765747},{"id":"https://openalex.org/keywords/schr\u00f6dingers-cat","display_name":"Schr\u00f6dinger's cat","score":0.4499616324901581},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.449618935585022},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.44862937927246094},{"id":"https://openalex.org/keywords/physical-system","display_name":"Physical system","score":0.4352068305015564},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.434145450592041},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3819255232810974},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3627258241176605},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16491588950157166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12017720937728882}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7040935754776001},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5655351877212524},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5104588270187378},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.5066972374916077},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4753163456916809},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.459532767534256},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.4522581100463867},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4500666856765747},{"id":"https://openalex.org/C194800363","wikidata":"https://www.wikidata.org/wiki/Q8588","display_name":"Schr\u00f6dinger's cat","level":2,"score":0.4499616324901581},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.449618935585022},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.44862937927246094},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.4352068305015564},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.434145450592041},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3819255232810974},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3627258241176605},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16491588950157166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12017720937728882},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14070481","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070481","pdf_url":"https://www.mdpi.com/2075-1680/14/7/481/pdf?version=1750414965","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:086be128b99d4702abb8786b740664cd","is_oa":true,"landing_page_url":"https://doaj.org/article/086be128b99d4702abb8786b740664cd","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 7, p 481 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14070481","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070481","pdf_url":"https://www.mdpi.com/2075-1680/14/7/481/pdf?version=1750414965","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G1589553732","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G3338836700","display_name":null,"funder_award_id":"04/2021","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G3601516360","display_name":null,"funder_award_id":"Brazil","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G4821329654","display_name":null,"funder_award_id":"GNAMPA","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G4845925241","display_name":null,"funder_award_id":"E5324001950001","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G5616681010","display_name":null,"funder_award_id":"2022/16407-1","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G8030638245","display_name":null,"funder_award_id":"2022/16097-2","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G8294567478","display_name":null,"funder_award_id":"4/2021","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G8315001488","display_name":null,"funder_award_id":"2022/16407-1","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G8920261182","display_name":null,"funder_award_id":"04/2021","funder_id":"https://openalex.org/F4320323350","funder_display_name":"Funda\u00e7\u00e3o de Apoio \u00e0 Pesquisa do Distrito Federal"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323350","display_name":"Funda\u00e7\u00e3o de Apoio \u00e0 Pesquisa do Distrito Federal","ror":"https://ror.org/04djvx395"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411494722.pdf","grobid_xml":"https://content.openalex.org/works/W4411494722.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W348555340","https://openalex.org/W744450657","https://openalex.org/W1759931293","https://openalex.org/W1966174732","https://openalex.org/W1972594862","https://openalex.org/W1981116812","https://openalex.org/W1981619409","https://openalex.org/W1982258462","https://openalex.org/W2002068176","https://openalex.org/W2007188481","https://openalex.org/W2007459766","https://openalex.org/W2018003055","https://openalex.org/W2027875590","https://openalex.org/W2034409564","https://openalex.org/W2035068227","https://openalex.org/W2037941539","https://openalex.org/W2039117838","https://openalex.org/W2046981059","https://openalex.org/W2054915577","https://openalex.org/W2078611265","https://openalex.org/W2080513630","https://openalex.org/W2081559794","https://openalex.org/W2090930259","https://openalex.org/W2148660036","https://openalex.org/W2149188355","https://openalex.org/W2149429567","https://openalex.org/W2315149965","https://openalex.org/W2603154707","https://openalex.org/W2963056571","https://openalex.org/W2963108684","https://openalex.org/W2963845416","https://openalex.org/W2969794561","https://openalex.org/W3000100337","https://openalex.org/W3048192409","https://openalex.org/W3160729122","https://openalex.org/W4233002841","https://openalex.org/W4395045033","https://openalex.org/W4400135056","https://openalex.org/W4405485546","https://openalex.org/W6780392976","https://openalex.org/W6809974339"],"related_works":["https://openalex.org/W2890439196","https://openalex.org/W4294608162","https://openalex.org/W3037639758","https://openalex.org/W4288640166","https://openalex.org/W2610621994","https://openalex.org/W153724988","https://openalex.org/W4302122319","https://openalex.org/W930414082","https://openalex.org/W588825723","https://openalex.org/W2349865015"],"abstract_inverted_index":{"In":[0,20],"this":[1],"paper":[2],"we":[3,26,61],"discuss":[4],"some":[5],"results":[6],"on":[7,102],"the":[8,22,33,37,42,47,59,73,78,85,103,106,112],"existence":[9,86],"of":[10,50,77,87,105],"solutions":[11,31],"for":[12,36],"an":[13,64,94],"elliptic":[14],"system":[15,23],"appearing":[16],"in":[17,32,63,111],"physical":[18],"sciences.":[19],"particular":[21],"appears":[24],"when":[25],"look":[27],"at":[28],"standing":[29],"wave":[30],"electrostatic":[34],"situation":[35],"Schr\u00f6dinger":[38],"equation":[39],"coupled,":[40],"with":[41,46],"minimal":[43,89],"coupling":[44],"rule,":[45],"electromagnetic":[48],"equations":[49],"Born\u2013Infeld":[51],"theory.":[52],"Many":[53],"difficulties":[54],"appear,":[55],"especially":[56],"due":[57],"to":[58,72,83],"fact":[60],"are":[62,81],"unbounded":[65],"domain":[66],"(the":[67],"whole":[68],"space":[69],"R3)":[70],"and":[71],"intrinsic":[74],"nonlinear":[75],"nature":[76],"equations.":[79],"We":[80],"able":[82],"prove":[84],"a":[88],"energy":[90],"solution":[91],"by":[92],"showing":[93],"approximating":[95],"procedure":[96],"that":[97],"can":[98],"be":[99],"adapted":[100],"depending":[101],"value":[104],"parameter":[107],"p,":[108],"which":[109],"is":[110],"nonlinearity.":[113]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}