{"id":"https://openalex.org/W7225833645","doi":"https://doi.org/10.1007/s41808-026-00532-x","title":"Ground states for critical fractional p-Laplacian Kirchhoff-type problems","display_name":"Ground states for critical fractional p-Laplacian Kirchhoff-type problems","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225833645","doi":"https://doi.org/10.1007/s41808-026-00532-x"},"language":"en","primary_location":{"id":"doi:10.1007/s41808-026-00532-x","doi":"https://doi.org/10.1007/s41808-026-00532-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41808-026-00532-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41808-026-00532-x.pdf","source":{"id":"https://openalex.org/S4210222994","display_name":"Journal of Elliptic and Parabolic Equations","issn_l":"2296-9039","issn":["2296-9039","2296-9020"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Elliptic and Parabolic Equations","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s41808-026-00532-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030826459","display_name":"Eduardo Dias Lima","orcid":"https://orcid.org/0009-0000-2078-3602","observed_orcids":["https://orcid.org/0009-0000-2078-3602"]},"institutions":[{"id":"https://openalex.org/I4387152431","display_name":"Universidade Federal do Norte do Tocantins","ror":"https://ror.org/04stx0g16","country_code":"BR","type":"education","lineage":["https://openalex.org/I4387152431"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Eduardo D. Lima","raw_affiliation_strings":["Universidade Federal do Norte do Tocantins, UFNT, Aragua\u00edna, TO, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Federal do Norte do Tocantins, UFNT, Aragua\u00edna, TO, Brazil","institution_ids":["https://openalex.org/I4387152431"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144349616","display_name":"Jefferson L. A. Oliveira","orcid":"https://orcid.org/0009-0003-4755-2400","observed_orcids":["https://orcid.org/0009-0003-4755-2400"]},"institutions":[{"id":"https://openalex.org/I41458283","display_name":"Universidade Federal do Tocantins","ror":"https://ror.org/053xy8k29","country_code":"BR","type":"education","lineage":["https://openalex.org/I41458283"]},{"id":"https://openalex.org/I4387152431","display_name":"Universidade Federal do Norte do Tocantins","ror":"https://ror.org/04stx0g16","country_code":"BR","type":"education","lineage":["https://openalex.org/I4387152431"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jefferson L. A. Oliveira","raw_affiliation_strings":["Universidade Federal do Norte do Tocantins, UFNT, Aragua\u00edna, TO, Brazil","Universidade Federal do Tocantins, UFT, Arraias, TO, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Federal do Norte do Tocantins, UFNT, Aragua\u00edna, TO, Brazil","institution_ids":["https://openalex.org/I4387152431"]},{"raw_affiliation_string":"Universidade Federal do Tocantins, UFT, Arraias, TO, Brazil","institution_ids":["https://openalex.org/I41458283"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5161434988","display_name":"Jos\u00e9 C. Oliveira","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I41458283","display_name":"Universidade Federal do Tocantins","ror":"https://ror.org/053xy8k29","country_code":"BR","type":"education","lineage":["https://openalex.org/I41458283"]},{"id":"https://openalex.org/I4387152431","display_name":"Universidade Federal do Norte do Tocantins","ror":"https://ror.org/04stx0g16","country_code":"BR","type":"education","lineage":["https://openalex.org/I4387152431"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 C. Oliveira","raw_affiliation_strings":["Universidade Federal do Norte do Tocantins, UFNT, Aragua\u00edna, TO, Brazil","Universidade Federal do Tocantins, UFT, Arraias, TO, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Federal do Norte do Tocantins, UFNT, Aragua\u00edna, TO, Brazil","institution_ids":["https://openalex.org/I4387152431"]},{"raw_affiliation_string":"Universidade Federal do Tocantins, UFT, Arraias, TO, Brazil","institution_ids":["https://openalex.org/I41458283"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030826459"],"corresponding_institution_ids":["https://openalex.org/I4387152431"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":{"value":3390,"currency":"USD","value_usd":3390},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/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"}},{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","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":[],"concepts":[{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.6204000115394592},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4542999863624573},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.44369998574256897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42080000042915344},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3869999945163727},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32350000739097595},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28929999470710754},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.2337999939918518},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22949999570846558},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.22220000624656677}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s41808-026-00532-x","doi":"https://doi.org/10.1007/s41808-026-00532-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41808-026-00532-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41808-026-00532-x.pdf","source":{"id":"https://openalex.org/S4210222994","display_name":"Journal of Elliptic and Parabolic Equations","issn_l":"2296-9039","issn":["2296-9039","2296-9020"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Elliptic and Parabolic Equations","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s41808-026-00532-x","doi":"https://doi.org/10.1007/s41808-026-00532-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s41808-026-00532-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s41808-026-00532-x.pdf","source":{"id":"https://openalex.org/S4210222994","display_name":"Journal of Elliptic and Parabolic Equations","issn_l":"2296-9039","issn":["2296-9039","2296-9020"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Elliptic and Parabolic Equations","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225833645.pdf","grobid_xml":"https://content.openalex.org/works/W7225833645.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W399101656","https://openalex.org/W779605620","https://openalex.org/W1511944115","https://openalex.org/W1973748816","https://openalex.org/W1977750299","https://openalex.org/W1996518052","https://openalex.org/W2011095781","https://openalex.org/W2066046051","https://openalex.org/W2070188765","https://openalex.org/W2084217877","https://openalex.org/W2287593028","https://openalex.org/W2523523424","https://openalex.org/W2561647999","https://openalex.org/W2767443677","https://openalex.org/W2788747430","https://openalex.org/W2806469065","https://openalex.org/W2925162015","https://openalex.org/W2967071869","https://openalex.org/W3159639140","https://openalex.org/W3193832935","https://openalex.org/W4294631610","https://openalex.org/W4366169344","https://openalex.org/W4389705501","https://openalex.org/W4400156625","https://openalex.org/W4404664669","https://openalex.org/W4409284664"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4],"study":[5],"the":[6,14],"existence":[7],"of":[8],"a":[9,71],"ground":[10],"state":[11],"solution":[12],"for":[13],"nondegenerate":[15],"fractional":[16],"p":[17,48,49,54,65,86,108,115,121,137,141],"-Kirchhoff":[18],"equation":[19],"$$":[20,39,105],"\\left(":[21],"\\alpha":[22],"+\\beta":[23],"[u]_{s,p}^p\\right)":[24],"(-\\Delta":[25],")_p^s":[26],"u":[27,44,56,63,68,76,81,84,91],"+":[28,33,41,57,82,110],"V(x)|u|^{p-2}u":[29],"=":[30,69],"\\lambda":[31],"a(x)|u|^{q-2}u":[32],"|u|^{p_s^*-2}u\\,\\,":[34],"\\text":[35],"{in}\\,\\,":[36],"\\mathbb":[37],"{R}^N\\!,":[38],"\u03b1":[40,129],"\u03b2":[42,131],"[":[43],"]":[45],"s":[46,55,87,100,114,120,142],",":[47,95,103,112,122,128,130],"(":[50,59,72],"-":[51,66,79,89],"\u0394":[52],")":[53,61,74],"V":[58],"x":[60,73],"|":[62,64,75,77,83,85],"2":[67,80,90,119,136],"\u03bb":[70,127],"q":[78,139],"\u2217":[88,143],"in":[92],"R":[93],"N":[94,117],"where":[96],"$$0<s<1$$":[97],"0":[98,133],"<":[99,101,107,109,116,118,138,140],"1":[102,106],"$$1<p<\\!+\\infty":[104],"\u221e":[111],"$$sp<N<2sp$$":[113],"$$\\lambda":[123],",\\alpha":[124],",\\beta":[125],">0$$":[126],">":[132],"and":[134],"$$2p<q<p_s^*$$":[135],".":[144],"Here":[145],"$$[u]_{s,p}$$":[146]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}