{"id":"https://openalex.org/W7142113412","doi":"https://doi.org/10.1016/j.aml.2026.109958","title":"Existence and multiplicity of solutions to a critical fourth-order elliptic equation with logarithmic perturbation","display_name":"Existence and multiplicity of solutions to a critical fourth-order elliptic equation with logarithmic perturbation","publication_year":2026,"publication_date":"2026-03-28","ids":{"openalex":"https://openalex.org/W7142113412","doi":"https://doi.org/10.1016/j.aml.2026.109958"},"language":"en","primary_location":{"id":"doi:10.1016/j.aml.2026.109958","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.aml.2026.109958","pdf_url":null,"source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","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/A5130869671","display_name":"Qian Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qian Zhang","raw_affiliation_strings":["School of Mathematics, Jilin University, Changchun 130012, PR China"],"raw_orcid":"https://orcid.org/0009-0001-4045-888X","affiliations":[{"raw_affiliation_string":"School of Mathematics, Jilin University, Changchun 130012, PR China","institution_ids":["https://openalex.org/I194450716"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5130849451","display_name":"Yuzhu Han","orcid":null},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuzhu Han","raw_affiliation_strings":["School of Mathematics, Jilin University, Changchun 130012, PR China"],"raw_orcid":"https://orcid.org/0000-0003-4215-7586","affiliations":[{"raw_affiliation_string":"School of Mathematics, Jilin University, Changchun 130012, PR China","institution_ids":["https://openalex.org/I194450716"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5130849451"],"corresponding_institution_ids":["https://openalex.org/I194450716"],"apc_list":{"value":3800,"currency":"USD","value_usd":3800},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.33061871,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"179","issue":null,"first_page":"109958","last_page":"109958"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.6848000288009644,"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":0.6848000288009644,"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":0.26669999957084656,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.004600000102072954,"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/multiplicity","display_name":"Multiplicity (mathematics)","score":0.736299991607666},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6000999808311462},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5303999781608582},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.5149999856948853},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.3303000032901764},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.29100000858306885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8452000021934509},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.736299991607666},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6000999808311462},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5374000072479248},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5303999781608582},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.5149999856948853},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.29100000858306885},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2904999852180481},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27970001101493835},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C12516240","wikidata":"https://www.wikidata.org/wiki/Q5641621","display_name":"Half-period ratio","level":5,"score":0.26600000262260437},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2630999982357025},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26019999384880066}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.aml.2026.109958","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.aml.2026.109958","pdf_url":null,"source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7369688153266907,"display_name":"Climate action","id":"https://metadata.un.org/sdg/13"}],"awards":[{"id":"https://openalex.org/G3406403891","display_name":null,"funder_award_id":"2020YFA0714101","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2038928461","https://openalex.org/W2058270372","https://openalex.org/W2066046051","https://openalex.org/W2077629107","https://openalex.org/W4321456191","https://openalex.org/W4362660255","https://openalex.org/W4383956878","https://openalex.org/W4392911609","https://openalex.org/W4394880623","https://openalex.org/W4417131371"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-03-29T00:00:00"}