{"id":"https://openalex.org/W2135302782","doi":"https://doi.org/10.4171/rmi/537","title":"Bound state solutions for a class of nonlinear Schr\u00f6dinger equations","display_name":"Bound state solutions for a class of nonlinear Schr\u00f6dinger equations","publication_year":2008,"publication_date":"2008-04-30","ids":{"openalex":"https://openalex.org/W2135302782","doi":"https://doi.org/10.4171/rmi/537","mag":"2135302782"},"language":"en","primary_location":{"id":"doi:10.4171/rmi/537","doi":"https://doi.org/10.4171/rmi/537","is_oa":true,"landing_page_url":"https://doi.org/10.4171/rmi/537","pdf_url":"https://ems.press/content/serial-article-files/4721","source":{"id":"https://openalex.org/S16719760","display_name":"Revista Matem\u00e1tica Iberoamericana","issn_l":"0213-2230","issn":["0213-2230","2235-0616"],"is_oa":false,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-2","latindex","norway-2","oarl","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310321816","host_organization_name":"Royal Spanish Mathematical Society","host_organization_lineage":["https://openalex.org/P4310321816"],"host_organization_lineage_names":["Royal Spanish Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Revista Matem\u00e1tica Iberoamericana","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://ems.press/content/serial-article-files/4721","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033040146","display_name":"Denis Bonheure","orcid":"https://orcid.org/0000-0001-5149-4328","observed_orcids":["https://orcid.org/0000-0001-5149-4328"]},"institutions":[{"id":"https://openalex.org/I132053463","display_name":"Universit\u00e9 Libre de Bruxelles","ror":"https://ror.org/01r9htc13","country_code":"BE","type":"education","lineage":["https://openalex.org/I132053463"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Denis Bonheure","raw_affiliation_strings":["Universit\u00e9 libre de Bruxelles, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-5149-4328","affiliations":[{"raw_affiliation_string":"Universit\u00e9 libre de Bruxelles, Belgium","institution_ids":["https://openalex.org/I132053463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008182807","display_name":"Jean Van Schaftingen","orcid":"https://orcid.org/0000-0002-5797-9358","observed_orcids":["https://orcid.org/0000-0002-5797-9358"]},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]},{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Jean Van Schaftingen","raw_affiliation_strings":["Universit\u00e9 Catholique de Louvain, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Catholique de Louvain, Belgium","institution_ids":["https://openalex.org/I95674353","https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.2814,"has_fulltext":true,"cited_by_count":47,"citation_normalized_percentile":{"value":0.96563707,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"24","issue":"1","first_page":"297","last_page":"351"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":9.999999747378752e-05,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0,"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-schrodinger-equation","display_name":"nonlinear Schr\u00f6dinger equation","score":0.8999999761581421},{"id":"https://openalex.org/keywords/bound-state-solutions","display_name":"bound state solutions","score":0.9160000085830688},{"id":"https://openalex.org/keywords/positive-solutions","display_name":"positive solutions","score":0.8769999742507935},{"id":"https://openalex.org/keywords/semiclassical-limit","display_name":"semiclassical limit","score":0.8999999761581421},{"id":"https://openalex.org/keywords/vanishing-potentials","display_name":"vanishing potentials","score":0.7870000004768372},{"id":"https://openalex.org/keywords/local-minima","display_name":"local minima","score":0.5720000267028809},{"id":"https://openalex.org/keywords/ground-state","display_name":"ground state","score":0.6420000195503235},{"id":"https://openalex.org/keywords/subcritical-exponent","display_name":"subcritical exponent","score":0.6510000228881836},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.49399998784065247}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.7011608481407166},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6824479103088379},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5565052628517151},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5048040151596069},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4753389358520508},{"id":"https://openalex.org/C174084160","wikidata":"https://www.wikidata.org/wiki/Q908049","display_name":"Bound state","level":2,"score":0.43946659564971924},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42029470205307007},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34321144223213196},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2602912187576294},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15764716267585754},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07210758328437805},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07038789987564087}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.4171/rmi/537","doi":"https://doi.org/10.4171/rmi/537","is_oa":true,"landing_page_url":"https://doi.org/10.4171/rmi/537","pdf_url":"https://ems.press/content/serial-article-files/4721","source":{"id":"https://openalex.org/S16719760","display_name":"Revista Matem\u00e1tica Iberoamericana","issn_l":"0213-2230","issn":["0213-2230","2235-0616"],"is_oa":false,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-2","latindex","norway-2","oarl","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310321816","host_organization_name":"Royal Spanish Mathematical Society","host_organization_lineage":["https://openalex.org/P4310321816"],"host_organization_lineage_names":["Royal Spanish Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Revista Matem\u00e1tica Iberoamericana","raw_type":"journal-article"},{"id":"pmh:oai:dipot.ulb.ac.be:2013/49375","doi":null,"is_oa":false,"landing_page_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/49375/1/9fcfd510f9f28ecb84.pdf","pdf_url":"https://dipot.ulb.ac.be/dspace/bitstream/2013/49375/1/9fcfd510f9f28ecb84.pdf","source":{"id":"https://openalex.org/S4306401063","display_name":"D\u00e9p\u00f4t institutionnel de l'Universit\u00e9 libre de Bruxelles (Universit\u00e9 Libre de Bruxelles)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I132053463","host_organization_name":"Universit\u00e9 Libre de Bruxelles","host_organization_lineage":["https://openalex.org/I132053463"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Revista matem\u00e1tica iberoamericana, 24 (1","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CULeuclid:euclid.rmi/1216247103","doi":null,"is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.rmi/1216247103","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:dial.uclouvain.be:boreal:36445","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/36445","pdf_url":null,"source":{"id":"https://openalex.org/S4306401974","display_name":"DIAL (Catholic University of Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Revista Matematica Iberoamericana, Vol. 24, no. 1, p. 297-351 (2008)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.4171/rmi/537","doi":"https://doi.org/10.4171/rmi/537","is_oa":true,"landing_page_url":"https://doi.org/10.4171/rmi/537","pdf_url":"https://ems.press/content/serial-article-files/4721","source":{"id":"https://openalex.org/S16719760","display_name":"Revista Matem\u00e1tica Iberoamericana","issn_l":"0213-2230","issn":["0213-2230","2235-0616"],"is_oa":false,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-2","latindex","norway-2","oarl","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310321816","host_organization_name":"Royal Spanish Mathematical Society","host_organization_lineage":["https://openalex.org/P4310321816"],"host_organization_lineage_names":["Royal Spanish Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Revista Matem\u00e1tica Iberoamericana","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320329819","display_name":"Fonds Sp\u00e9ciaux de Recherche","ror":"https://ror.org/02hcmqg97"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2135302782.pdf","grobid_xml":"https://content.openalex.org/works/W2135302782.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W30275232","https://openalex.org/W593537426","https://openalex.org/W1537483744","https://openalex.org/W1546651112","https://openalex.org/W1586623601","https://openalex.org/W1588528702","https://openalex.org/W1968782046","https://openalex.org/W1973605878","https://openalex.org/W1977632986","https://openalex.org/W1987572283","https://openalex.org/W1987917148","https://openalex.org/W1994676947","https://openalex.org/W1996167460","https://openalex.org/W1998008832","https://openalex.org/W2007460600","https://openalex.org/W2018833240","https://openalex.org/W2021833235","https://openalex.org/W2023868857","https://openalex.org/W2038032040","https://openalex.org/W2046351080","https://openalex.org/W2051721169","https://openalex.org/W2058270372","https://openalex.org/W2061613404","https://openalex.org/W2066775064","https://openalex.org/W2068534708","https://openalex.org/W2070165231","https://openalex.org/W2079595328","https://openalex.org/W2085504465","https://openalex.org/W2094187519","https://openalex.org/W2104523496","https://openalex.org/W2163181731","https://openalex.org/W2168853925","https://openalex.org/W2509548217","https://openalex.org/W2572075230","https://openalex.org/W2605833619","https://openalex.org/W2916567905","https://openalex.org/W3103465570","https://openalex.org/W3217362339","https://openalex.org/W4232306901","https://openalex.org/W4285719527","https://openalex.org/W6600421821","https://openalex.org/W6600577311","https://openalex.org/W6831801130"],"related_works":["https://openalex.org/W2066775064","https://openalex.org/W2025311485","https://openalex.org/W7099096996","https://openalex.org/W1994676947","https://openalex.org/W1994644138","https://openalex.org/W1965523783","https://openalex.org/W2069920060","https://openalex.org/W2031539634","https://openalex.org/W2055950496","https://openalex.org/W2015575105"],"abstract_inverted_index":{"We":[0],"deal":[1],"with":[2],"the":[3,19,50,56,66,77,87,99,116],"existence":[4,51,88],"of":[5,13,18,52,89,98,119],"positive":[6,35],"bound":[7,90],"state":[8,91],"solutions":[9,92,121],"for":[10,81],"a":[11,45],"class":[12],"stationary":[14],"nonlinear":[15],"Schr\u00f6dinger":[16],"equations":[17],"form":[20],"$$":[21],"-\\varepsilon^2\\Delta":[22],"u":[23,26],"+":[24],"V(x)":[25],"=":[27,103],"K(x)":[28],"u^p,\\qquad":[29],"x\\in\\mathbb{R}^N,":[30],"where":[31,107],"V,":[32],"K":[33,69],"are":[34],"continuous":[36],"functions":[37],"and":[38,65],"p":[39],">":[40],"1":[41],"is":[42,59,113],"subcritical,":[43],"in":[44],"framework":[46],"which":[47],"may":[48],"exclude":[49],"ground":[53],"states.":[54],"Namely,":[55],"potential":[57],"V":[58],"allowed":[60],"to":[61,73,115,125],"vanish":[62],"at":[63],"infinity":[64],"competing":[67],"function":[68,101],"does":[70],"not":[71],"have":[72],"be":[74],"bounded.":[75],"In":[76],"\\\\emph{semi-classical":[78],"limit},":[79],"i.e.":[80],"\\varepsilon\\sim":[82],"0":[83],",":[84,106],"we":[85],"prove":[86],"localized":[93],"around":[94],"local":[95],"minimum":[96],"points":[97],"auxiliary":[100],"\\mathcal{A}":[102],"V^\\theta":[104],"K^{-\\frac{2}{p-1}}":[105],"\\theta=(p+1)/(p-1)-N/2":[108],".":[109],"A":[110],"special":[111],"attention":[112],"devoted":[114],"qualitative":[117],"properties":[118],"these":[120],"as":[122],"\\varepsilon$":[123],"goes":[124],"zero.":[126]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2016-06-24T00:00:00"}
