{"id":"https://openalex.org/W7223663832","doi":"https://doi.org/10.48550/arxiv.2610.32274","title":"Semilinear Schr\u00f6dinger equation with harmonic potential and combined power-type nonlinearities","display_name":"Semilinear Schr\u00f6dinger equation with harmonic potential and combined power-type nonlinearities","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223663832","doi":"https://doi.org/10.48550/arxiv.2610.32274"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.32274","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32274","pdf_url":"https://arxiv.org/pdf/2610.32274","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.32274","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080663228","display_name":"Jiangbo Han","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Han, Jiangbo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093835173","display_name":"Runzhang Xu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Runzhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5159667769","display_name":"Chao Yang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Chao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9994999766349792,"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":0.9994999766349792,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.00039999998989515007,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/semilinear-schrodinger-equation","display_name":"semilinear Schr\u00f6dinger equation","score":1.0},{"id":"https://openalex.org/keywords/harmonic-potential","display_name":"harmonic potential","score":0.9890000224113464},{"id":"https://openalex.org/keywords/cauchy-problem","display_name":"Cauchy problem","score":0.9559999704360962},{"id":"https://openalex.org/keywords/global-existence","display_name":"global existence","score":0.8379999995231628},{"id":"https://openalex.org/keywords/finite-time-blow-up","display_name":"finite-time blow-up","score":0.984000027179718},{"id":"https://openalex.org/keywords/initial-energy","display_name":"initial energy","score":0.640999972820282},{"id":"https://openalex.org/keywords/energy-functional","display_name":"energy functional","score":0.48500001430511475}],"concepts":[{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.6029000282287598},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.597599983215332},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5148000121116638},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.484499990940094},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4372999966144562},{"id":"https://openalex.org/C2991656669","wikidata":"https://www.wikidata.org/wiki/Q677864","display_name":"Harmonic potential","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.41819998621940613},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.35670000314712524},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C84551667","wikidata":"https://www.wikidata.org/wiki/Q155640","display_name":"Potential energy","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C97985569","wikidata":"https://www.wikidata.org/wiki/Q216861","display_name":"Calculus of variations","level":2,"score":0.29899999499320984},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.29899999499320984},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.289000004529953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28859999775886536},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28700000047683716}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.32274","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32274","pdf_url":"https://arxiv.org/pdf/2610.32274","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.32274","doi":"https://doi.org/10.48550/arxiv.2610.32274","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.32274","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.32274","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32274","pdf_url":"https://arxiv.org/pdf/2610.32274","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223663832.pdf","grobid_xml":"https://content.openalex.org/works/W7223663832.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2040430869","https://openalex.org/W1985020240","https://openalex.org/W2022208565","https://openalex.org/W1991230386","https://openalex.org/W2382511397","https://openalex.org/W4297963361","https://openalex.org/W2032042795","https://openalex.org/W3161792645","https://openalex.org/W3186276735","https://openalex.org/W2029217381"],"abstract_inverted_index":{"We":[0,57,156,227],"study":[1],"the":[2,6,50,68,135,158,169,175,202,216,234],"Cauchy":[3],"problem":[4],"for":[5,53,117,150,201,224,233],"semilinear":[7],"Schr\u00f6dinger":[8,204],"equation":[9],"with":[10,121],"a":[11,208,230],"harmonic":[12],"potential":[13],"and":[14,44,71,83,110,143,171],"combined":[15],"power-type":[16],"nonlinearities.":[17],"The":[18],"goal":[19],"is":[20,185],"to":[21,27,77,86,145,214],"classify":[22,147,215],"initial":[23,88,104,119,148,183,195],"data":[24,89,120,149],"that":[25,90,116,181],"lead":[26],"either":[28],"global":[29,93,151,220],"existence":[30,152,221],"or":[31,95,153,222],"blowup":[32],"solutions":[33,94,124],"by":[34,63],"using":[35],"an":[36,197],"enhanced":[37],"cross-constrained":[38,80],"variational":[39,47,61,81,141],"theory.":[40],"First,":[41],"we":[42,101,114,137,164,179,206],"review":[43],"analyze":[45,165],"this":[46,238],"approach,":[48],"pinpointing":[49],"main":[51],"issue":[52,199],"our":[54,161,225],"specific":[55],"problem.":[56,240],"then":[58],"introduce":[59],"new":[60,140],"structures":[62],"carefully":[64],"selecting":[65],"terms":[66],"in":[67,92,127],"energy":[69,105,170,184,213],"functional":[70],"adjusting":[72],"their":[73,132],"weights,":[74],"enabling":[75],"us":[76],"create":[78],"eight":[79],"combinations":[82,167],"related":[84],"manifolds":[85],"distinguish":[87],"result":[91],"finite-time":[96,154],"blowup.":[97,155],"Using":[98],"these":[99,139],"structures,":[100],"examine":[102],"three":[103],"levels:":[106],"negative,":[107],"non-negative":[108],"low,":[109],"high":[111,194],"energy.":[112],"Notably,":[113],"prove":[115],"any":[118],"negative":[122],"energy,":[123,196],"blow":[125],"up":[126],"finite":[128],"time":[129],"regardless":[130],"of":[131,160,168,212],"size.":[133],"Throughout":[134],"study,":[136],"utilize":[138],"frameworks":[142],"functionals":[144,191],"systematically":[146],"highlight":[157],"comprehensiveness":[159],"approach":[162],"as":[163],"numerous":[166],"mass":[172],"terms,":[173],"despite":[174],"complexity":[176],"involved.":[177],"Interestingly,":[178],"find":[180],"when":[182],"minimized,":[186],"classifications":[187],"based":[188],"on":[189],"different":[190],"coincide.":[192],"For":[193],"unresolved":[198],"even":[200],"standard":[203,235],"equation,":[205],"develop":[207],"strategy":[209],"controlling":[210],"bounds":[211],"solution":[217],"dynamics,":[218],"including":[219],"blowup,":[223],"model.":[226],"also":[228],"provide":[229],"complete":[231],"proof":[232],"case":[236],"addressing":[237],"open":[239]},"counts_by_year":[],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2026-10-27T00:00:00"}
