{"id":"https://openalex.org/W7214102136","doi":"https://doi.org/10.48550/arxiv.2609.26585","title":"A unifying zero-mass equation","display_name":"A unifying zero-mass equation","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214102136","doi":"https://doi.org/10.48550/arxiv.2609.26585"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.26585","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26585","pdf_url":"https://arxiv.org/pdf/2609.26585","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.26585","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001888163","display_name":"Kanishka Perera","orcid":"https://orcid.org/0000-0001-6168-247X","observed_orcids":["https://orcid.org/0000-0001-6168-247X"]},"institutions":[{"id":"https://openalex.org/I106959904","display_name":"Florida Institute of Technology","ror":"https://ror.org/04atsbb87","country_code":"US","type":"education","lineage":["https://openalex.org/I106959904"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Perera, Kanishka","raw_affiliation_strings":["Department of Mathematics Florida Institute of Technology 150 W University Blvd , Melbourne , FL 32901-6975 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics Florida Institute of Technology 150 W University Blvd , Melbourne , FL 32901-6975 , USA","institution_ids":["https://openalex.org/I106959904"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001888163"],"corresponding_institution_ids":["https://openalex.org/I106959904"],"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/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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":9.999999747378752e-05,"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/radial-solutions","display_name":"radial solutions","score":0.5630000233650208},{"id":"https://openalex.org/keywords/compact-embedding","display_name":"compact embedding","score":0.5450000166893005},{"id":"https://openalex.org/keywords/pohozaev-identity","display_name":"Pohozaev identity","score":0.9909999966621399},{"id":"https://openalex.org/keywords/eigenvalue-problem","display_name":"eigenvalue problem","score":0.6140000224113464},{"id":"https://openalex.org/keywords/critical-exponents","display_name":"critical exponents","score":0.5979999899864197},{"id":"https://openalex.org/keywords/multiple-solutions","display_name":"multiplicity of solutions","score":0.6959999799728394}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7634000182151794},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6320000290870667},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5916000008583069},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.511900007724762},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.454800009727478},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.4171999990940094},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3474000096321106},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.33329999446868896},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C70985411","wikidata":"https://www.wikidata.org/wiki/Q2380676","display_name":"Integro-differential equation","level":4,"score":0.28790000081062317},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C135593079","wikidata":"https://www.wikidata.org/wiki/Q1750766","display_name":"Scale invariance","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C106214006","wikidata":"https://www.wikidata.org/wiki/Q1455898","display_name":"Well-posed problem","level":2,"score":0.2574999928474426},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.25540000200271606}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.26585","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26585","pdf_url":"https://arxiv.org/pdf/2609.26585","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.2609.26585","doi":"https://doi.org/10.48550/arxiv.2609.26585","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.26585","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:2609.26585","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26585","pdf_url":"https://arxiv.org/pdf/2609.26585","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/W7214102136.pdf","grobid_xml":"https://content.openalex.org/works/W7214102136.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7118767253","https://openalex.org/W7129094719"],"related_works":["https://openalex.org/W4401618145","https://openalex.org/W4401652015","https://openalex.org/W2964012014","https://openalex.org/W7095521369","https://openalex.org/W1554040819","https://openalex.org/W4407911670","https://openalex.org/W7129094719","https://openalex.org/W2937568832","https://openalex.org/W4200634547","https://openalex.org/W4415254627"],"abstract_inverted_index":{"We":[0,63],"introduce":[1],"the":[2,32,37,48,53,57,65,100,115,126,166,187],"nonlocal":[3],"zero-mass":[4],"equation":[5,46,59,189],"\\[":[6],"-":[7],"\u0394u":[8],"+":[9],"\u03a6_u(|x|)\\,":[10],"|u|^{p-2}\\,":[11],"u":[12],"=":[13,22],"f(u)":[14],"\\quad":[15],"\\text{in":[16],"}":[17],"{\\mathbb":[18],"R}^N,":[19],"\\qquad":[20],"\u03a6_u(r)":[21],"a":[23,83,87,92,96,110,136,144,151,174,182],"\\int_r^\\infty":[24],"\u03c1^{-b}\\,":[25],"h_u^{q-1}(\u03c1)\\,":[26],"d\u03c1,":[27],"\\]":[28],"where":[29],"$h_u(\u03c1)$":[30],"is":[31,135,160],"mass":[33],"of":[34,39,99,107,109,143],"$|u|^p$":[35],"in":[36,125,173,190],"ball":[38],"radius":[40],"$\u03c1$.":[41],"For":[42],"radial":[43,80,153],"functions,":[44],"this":[45],"includes":[47],"defocusing":[49],"inverse-power":[50],"Schr\u00f6dinger":[51],"equation,":[52,55],"Chern-Simons-Schr\u00f6dinger":[54],"and":[56,69,76,91,119,122,129,177],"Schr\u00f6dinger-Poisson-Slater":[58,188],"as":[60],"special":[61],"cases.":[62],"develop":[64],"associated":[66],"ball-mass":[67],"Lebesgue":[68],"Sobolev":[70],"spaces,":[71],"which":[72,149],"are":[73],"uniformly":[74],"convex,":[75],"prove":[77],"sharp":[78],"compact":[79],"embeddings":[81],"above":[82],"new":[84,145,179],"critical":[85,130],"exponent,":[86],"Br\u00e9zis-Lieb":[88],"type":[89,138,184],"splitting,":[90],"Poho\u017eaev":[93],"identity.":[94],"Exploiting":[95],"scaling":[97],"invariance":[98],"operator,":[101],"we":[102],"construct":[103],"an":[104,162],"unbounded":[105],"sequence":[106],"eigenvalues":[108],"scaled":[111,146],"eigenvalue":[112],"problem":[113],"using":[114],"Fadell-Rabinowitz":[116],"cohomological":[117],"index,":[118],"obtain":[120],"existence":[121],"multiplicity":[123],"results":[124,172],"subscaled,":[127],"superscaled,":[128],"regimes.":[131],"Our":[132],"main":[133],"result":[134,185],"Br\u00e9zis-Nirenberg":[137,183],"theorem,":[139,148],"proved":[140],"by":[141],"means":[142],"linking":[147],"gives":[150],"nontrivial":[152],"solution":[154],"for":[155,186],"every":[156],"$\u03bb>":[157],"0$":[158],"that":[159],"not":[161],"eigenvalue.":[163],"Specializing":[164],"to":[165],"three":[167],"models":[168],"recovers":[169],"several":[170],"known":[171],"unified":[175],"way":[176],"yields":[178],"ones,":[180],"including":[181],"dimensions":[191],"$N":[192],"\\ge":[193],"4$.":[194]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}
