{"id":"https://openalex.org/W4388534298","doi":"https://doi.org/10.1137/22m1521675","title":"Normalized Solutions for Schr\u00f6dinger Equations with Critical Exponential Growth in \\(\\boldsymbol{\\mathbb{R}^2}\\)","display_name":"Normalized Solutions for Schr\u00f6dinger Equations with Critical Exponential Growth in \\(\\boldsymbol{\\mathbb{R}^2}\\)","publication_year":2023,"publication_date":"2023-11-09","ids":{"openalex":"https://openalex.org/W4388534298","doi":"https://doi.org/10.1137/22m1521675"},"language":"en","primary_location":{"id":"doi:10.1137/22m1521675","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1521675","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100751926","display_name":"Sitong Chen","orcid":"https://orcid.org/0000-0003-2839-6070"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sitong Chen","raw_affiliation_strings":["School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People\u2019s Republic of China","School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People\u2019s Republic of China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People's Republic of China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105977470","display_name":"Vicen\u0163iu D. R\u0103dulescu","orcid":"https://orcid.org/0000-0003-4615-5537"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vicen\u0163iu D. R\u0103dulescu","raw_affiliation_strings":["Faculty of Applied Mathematics, AGH University of Science and Technology, Krak\u00f3w, Poland, and Department of Mathematics, University of Craiova, 200585 Craiova, Romania, and Brno University of Technology, Faculty of Electrical Engineering and Communication, Technick\u00e1, Brno 61600, Czech Republic, and School of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China, and Simion Stoilow Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Faculty of Applied Mathematics, AGH University of Science and Technology, Krak\u00f3w, Poland, and Department of Mathematics, University of Craiova, 200585 Craiova, Romania, and Brno University of Technology, Faculty of Electrical Engineering and Communication, Technick\u00e1, Brno 61600, Czech Republic, and School of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China, and Simion Stoilow Institute of Mathematics of the Romanian Academy, 010702 Bucharest, Romania","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069174584","display_name":"Xianhua Tang","orcid":"https://orcid.org/0000-0001-7963-0782"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianhua Tang","raw_affiliation_strings":["School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People\u2019s Republic of China","School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People\u2019s Republic of China","institution_ids":["https://openalex.org/I139660479"]},{"raw_affiliation_string":"School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People's Republic of China","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088748113","display_name":"Shuai Yuan","orcid":"https://orcid.org/0000-0002-4133-4934"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shuai Yuan","raw_affiliation_strings":["Corresponding author. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People\u2019s Republic of China, and Department of Mathematics, University of Craiova, 200585 Craiova, Romania"],"affiliations":[{"raw_affiliation_string":"Corresponding author. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, People\u2019s Republic of China, and Department of Mathematics, University of Craiova, 200585 Craiova, Romania","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100751926"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":12.5794,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.99549789,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"55","issue":"6","first_page":"7704","last_page":"7740"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9987999796867371,"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":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8063895106315613},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.6453899145126343},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5421465635299683},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.5141668319702148},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49211376905441284},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.4310497045516968}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8063895106315613},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.6453899145126343},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5421465635299683},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5141668319702148},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49211376905441284},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.4310497045516968}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1521675","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1521675","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3981215530","display_name":null,"funder_award_id":"2021JJ40703","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G4341340939","display_name":null,"funder_award_id":"12001542","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8580406415","display_name":null,"funder_award_id":"11971485","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W636566490","https://openalex.org/W652382442","https://openalex.org/W1597067391","https://openalex.org/W1638960425","https://openalex.org/W1968052459","https://openalex.org/W1987917148","https://openalex.org/W2001835483","https://openalex.org/W2013508090","https://openalex.org/W2013535418","https://openalex.org/W2037984616","https://openalex.org/W2038928461","https://openalex.org/W2043812901","https://openalex.org/W2078526850","https://openalex.org/W2509548217","https://openalex.org/W2916567905","https://openalex.org/W2963434478","https://openalex.org/W2973478527","https://openalex.org/W3004949492","https://openalex.org/W3021019254","https://openalex.org/W3038917085","https://openalex.org/W3080838889","https://openalex.org/W3085488395","https://openalex.org/W3096033897","https://openalex.org/W3127975849","https://openalex.org/W3127980000","https://openalex.org/W4232306901","https://openalex.org/W4244689643","https://openalex.org/W4244989263"],"related_works":["https://openalex.org/W4394883359","https://openalex.org/W1602624896","https://openalex.org/W1519862060","https://openalex.org/W1634993130","https://openalex.org/W2104564563","https://openalex.org/W32300376","https://openalex.org/W2794917831","https://openalex.org/W2013108996","https://openalex.org/W3023224836","https://openalex.org/W1990369157"],"abstract_inverted_index":{".For":[0],"any":[1],"\\(a\\gt":[2],"0\\),":[3],"we":[4,88,126],"study":[5],"the":[6,16,43,64,69,96,140,163,173],"existence":[7,92],"of":[8,63,77,84,98,107,114,131,175],"normalized":[9,99],"solutions":[10,14],"and":[11,57,68,112,134],"ground":[12],"state":[13],"to":[15,138,172],"following":[17],"Schr\u00f6dinger":[18,116],"equation":[19],"with":[20,118],"\\(L^2\\)-constraint:":[21],"\\(\\left\\{":[22],"\\begin{array}{ll}":[23],"-\\Delta":[24],"u+\\lambda":[25],"u=b(x)f(u)":[26],"&":[27],"x\\in":[28],"\\mathbb{R}^2,":[29],"\\\\":[30,32],"\\int_{\\mathbb{R}^2}u^2\\mathrm{d}x=a,":[31],"\\end{array}":[33],"\\right.\\)":[34],"where":[35],"\\(\\lambda":[36],"\\in":[37],"\\mathbb{R}\\)":[38],"is":[39],"a":[40,60],"Lagrange":[41],"multiplier,":[42],"potential":[44],"\\(b\\in":[45],"\\mathcal{C}(\\mathbb{R}^2,":[46],"(0,":[47],"\\infty":[48,53],"))\\)":[49],"satisfies":[50],"\\(0\\lt":[51],"\\lim_{|y|\\to":[52],"}b(y)\\leq":[54],"\\inf_{x\\in":[55],"\\mathbb{R}^2}b(x)\\)":[56],"appears":[58],"as":[59,104],"converse":[61],"direction":[62],"Rabinowitz-type":[65,119],"trapping":[66,120],"potential,":[67],"reaction":[70],"\\(f\\in":[71],"\\mathcal{C}(\\mathbb{R},\\mathbb{R})\\)":[72],"enjoys":[73],"critical":[74,110,165],"exponential":[75,180],"growth":[76],"Trudinger\u2013Moser":[78,164],"type.":[79],"Under":[80],"two":[81],"different":[82],"kinds":[83],"assumptions":[85],"on":[86],"\\(f\\),":[87],"prove":[89],"several":[90],"new":[91],"results,":[93],"which,":[94],"in":[95,123,162],"context":[97],"solutions,":[100],"can":[101],"be":[102],"considered":[103],"both":[105],"counterparts":[106],"planar":[108],"unconstrained":[109,115],"problems":[111,117,161],"extensions":[113],"potential.":[121],"Especially,":[122],"this":[124],"scenario,":[125],"develop":[127],"some":[128],"sharp":[129],"estimates":[130],"energy":[132],"levels":[133],"ingenious":[135],"analysis":[136],"techniques":[137,153],"restore":[139],"compactness":[141],"which":[142],"are":[143],"novel":[144],"even":[145],"for":[146],"\\(b(x)\\equiv\\)":[147],"constant.":[148],"We":[149],"believe":[150],"that":[151],"these":[152],"will":[154],"allow":[155],"not":[156],"only":[157],"treating":[158],"other":[159],"\\(L^2\\)-constrained":[160],"setting":[166],"but":[167],"also":[168],"generalizing":[169],"previous":[170],"results":[171],"case":[174],"variable":[176],"potentials.KeywordsSchr\u00f6dinger":[177],"equationnormalized":[178],"solutioncritical":[179],"growthTrudinger\u2013Moser":[181],"inequalityMSC":[182],"codes35J2035J6235Q55":[183]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":13}],"updated_date":"2026-03-25T14:56:36.534964","created_date":"2025-10-10T00:00:00"}