{"id":"https://openalex.org/W2997104354","doi":"https://doi.org/10.3390/sym12010076","title":"A Class of Critical Magnetic Fractional Kirchhoff Problems","display_name":"A Class of Critical Magnetic Fractional Kirchhoff Problems","publication_year":2020,"publication_date":"2020-01-02","ids":{"openalex":"https://openalex.org/W2997104354","doi":"https://doi.org/10.3390/sym12010076","mag":"2997104354"},"language":"en","primary_location":{"id":"doi:10.3390/sym12010076","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12010076","pdf_url":"https://www.mdpi.com/2073-8994/12/1/76/pdf?version=1578455765","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/1/76/pdf?version=1578455765","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012721019","display_name":"Jiabin Zuo","orcid":"https://orcid.org/0000-0002-5858-063X"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]},{"id":"https://openalex.org/I4210102505","display_name":"Jilin Engineering Normal University","ror":"https://ror.org/018gks972","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210102505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiabin Zuo","raw_affiliation_strings":["College of Science, Hohai University, Nanjing 211100, China","Faculty of Applied Sciences, Jilin Engineering Normal University, Changchun 130052, China"],"raw_orcid":"https://orcid.org/0000-0002-5858-063X","affiliations":[{"raw_affiliation_string":"College of Science, Hohai University, Nanjing 211100, China","institution_ids":["https://openalex.org/I163340411"]},{"raw_affiliation_string":"Faculty of Applied Sciences, Jilin Engineering Normal University, Changchun 130052, China","institution_ids":["https://openalex.org/I4210102505"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060709068","display_name":"Tianqing An","orcid":"https://orcid.org/0000-0002-1480-6983"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianqing An","raw_affiliation_strings":["College of Science, Hohai University, Nanjing 211100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hohai University, Nanjing 211100, China","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013690355","display_name":"Guoju Ye","orcid":"https://orcid.org/0000-0003-4671-049X"},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Guoju Ye","raw_affiliation_strings":["College of Science, Hohai University, Nanjing 211100, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hohai University, Nanjing 211100, China","institution_ids":["https://openalex.org/I163340411"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013690355"],"corresponding_institution_ids":["https://openalex.org/I163340411"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.1711,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.74683139,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"12","issue":"1","first_page":"76","last_page":"76"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9990000128746033,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/class","display_name":"Class (philosophy)","score":0.6561420559883118},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6306906938552856},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6123723983764648},{"id":"https://openalex.org/keywords/critical-point","display_name":"Critical point (mathematics)","score":0.5123423337936401},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49178722500801086},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.46003565192222595},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4274210035800934},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2538924515247345},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15090546011924744},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.06322947144508362}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6561420559883118},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6306906938552856},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6123723983764648},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.5123423337936401},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49178722500801086},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.46003565192222595},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4274210035800934},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2538924515247345},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15090546011924744},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.06322947144508362},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12010076","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12010076","pdf_url":"https://www.mdpi.com/2073-8994/12/1/76/pdf?version=1578455765","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:faaacff3bf4e4244896ee558f272671e","is_oa":true,"landing_page_url":"https://doaj.org/article/faaacff3bf4e4244896ee558f272671e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 1, p 76 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/1/76/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym12010076","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12010076","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12010076","pdf_url":"https://www.mdpi.com/2073-8994/12/1/76/pdf?version=1578455765","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5662048802","display_name":null,"funder_award_id":"BK20180500","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G5835706456","display_name":null,"funder_award_id":"2017B19714, 2017B07414, 2019B44914","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G7405719256","display_name":null,"funder_award_id":"2018YFC1508106","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G807328297","display_name":null,"funder_award_id":"201906710004","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1545761024","https://openalex.org/W1843205648","https://openalex.org/W1855169650","https://openalex.org/W1986408858","https://openalex.org/W2011176581","https://openalex.org/W2061118817","https://openalex.org/W2066046051","https://openalex.org/W2210818451","https://openalex.org/W2275286668","https://openalex.org/W2289180117","https://openalex.org/W2465759602","https://openalex.org/W2610841850","https://openalex.org/W2623035224","https://openalex.org/W2780546854","https://openalex.org/W2782403437","https://openalex.org/W2787489911","https://openalex.org/W2896189246","https://openalex.org/W2902211353","https://openalex.org/W2902574933","https://openalex.org/W2907937226","https://openalex.org/W2962989571","https://openalex.org/W2963613749","https://openalex.org/W2963808172","https://openalex.org/W2998393158","https://openalex.org/W3021722416","https://openalex.org/W3100253402","https://openalex.org/W3163575612","https://openalex.org/W4403556217","https://openalex.org/W6795519846"],"related_works":["https://openalex.org/W2154204858","https://openalex.org/W3101030220","https://openalex.org/W3209622820","https://openalex.org/W1570562499","https://openalex.org/W1630264349","https://openalex.org/W2382250648","https://openalex.org/W102371419","https://openalex.org/W3021583805","https://openalex.org/W2367363545","https://openalex.org/W2586383879"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"deal":[4],"with":[5],"the":[6,20,28,40,43],"existence":[7],"and":[8,23],"asymptotic":[9],"behavior":[10],"of":[11,42],"solutions":[12],"for":[13],"a":[14],"fractional":[15],"Kirchhoff":[16],"type":[17],"problem":[18],"involving":[19],"electromagnetic":[21],"fields":[22],"critical":[24,30],"nonlinearity":[25],"by":[26],"using":[27],"classical":[29],"point":[31],"theorem.":[32],"Meanwhile,":[33],"an":[34],"example":[35],"is":[36],"given":[37],"to":[38],"illustrate":[39],"application":[41],"main":[44],"result.":[45]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
