{"id":"https://openalex.org/W1997670972","doi":"https://doi.org/10.1155/2011/829107","title":"The Existence of Multiple Periodic Solutions of Nonautonomous Delay Differential Equations","display_name":"The Existence of Multiple Periodic Solutions of Nonautonomous Delay Differential Equations","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1997670972","doi":"https://doi.org/10.1155/2011/829107","mag":"1997670972"},"language":"en","primary_location":{"id":"doi:10.1155/2011/829107","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/829107","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/829107.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2011/829107.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066086505","display_name":"Huafeng Xiao","orcid":"https://orcid.org/0000-0002-1691-8735"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huafeng Xiao","raw_affiliation_strings":["College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China","College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008551483","display_name":"Bo Zheng","orcid":"https://orcid.org/0000-0003-4056-9114"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Zheng","raw_affiliation_strings":["College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China","College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China","institution_ids":["https://openalex.org/I37987034"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I37987034"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.08981595,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2011","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9991999864578247,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.8324848413467407},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.6923174262046814},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5748577117919922},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5686092972755432},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.5519673824310303},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.48619478940963745},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4632595181465149},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.4586278796195984},{"id":"https://openalex.org/keywords/comparison-theorem","display_name":"Comparison theorem","score":0.41932979226112366},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3663554787635803},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.17780336737632751},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09204164147377014}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8324848413467407},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.6923174262046814},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5748577117919922},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5686092972755432},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.5519673824310303},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.48619478940963745},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4632595181465149},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.4586278796195984},{"id":"https://openalex.org/C2779396167","wikidata":"https://www.wikidata.org/wiki/Q5156040","display_name":"Comparison theorem","level":2,"score":0.41932979226112366},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3663554787635803},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.17780336737632751},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09204164147377014},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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":4,"locations":[{"id":"doi:10.1155/2011/829107","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/829107","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/829107.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1313170515","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1313170515","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:829107","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2011/829107.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:414b459b01be4274b3148f365a777cce","is_oa":true,"landing_page_url":"https://doaj.org/article/414b459b01be4274b3148f365a777cce","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":"Journal of Applied Mathematics, Vol 2011 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2011/829107","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/829107","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/829107.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"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 Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1166721228","display_name":null,"funder_award_id":"11026059","funder_id":"https://openalex.org/F4320311429","funder_display_name":"Guangzhou Medical University"},{"id":"https://openalex.org/G1468641952","display_name":null,"funder_award_id":"11026059","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1666098831","display_name":null,"funder_award_id":"LYM09105","funder_id":"https://openalex.org/F4320327517","funder_display_name":"Foundation for Distinguished Young Talents in Higher Education of Guangdong"},{"id":"https://openalex.org/G2803658767","display_name":null,"funder_award_id":"LYM09105","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3049313368","display_name":null,"funder_award_id":"10A012","funder_id":"https://openalex.org/F4320311429","funder_display_name":"Guangzhou Medical University"},{"id":"https://openalex.org/G4765475510","display_name":null,"funder_award_id":"11026059","funder_id":"https://openalex.org/F4320327517","funder_display_name":"Foundation for Distinguished Young Talents in Higher Education of Guangdong"},{"id":"https://openalex.org/G7740704091","display_name":null,"funder_award_id":"10A012","funder_id":"https://openalex.org/F4320327517","funder_display_name":"Foundation for Distinguished Young Talents in Higher Education of Guangdong"},{"id":"https://openalex.org/G8897961675","display_name":null,"funder_award_id":"LYM09105","funder_id":"https://openalex.org/F4320311429","funder_display_name":"Guangzhou Medical University"},{"id":"https://openalex.org/G8933112250","display_name":null,"funder_award_id":"10A012","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320311429","display_name":"Guangzhou Medical University","ror":"https://ror.org/00zat6v61"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320327517","display_name":"Foundation for Distinguished Young Talents in Higher Education of Guangdong","ror":null},{"id":"https://openalex.org/F4320328715","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1997670972.pdf","grobid_xml":"https://content.openalex.org/works/W1997670972.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1964053068","https://openalex.org/W1969953268","https://openalex.org/W1976842194","https://openalex.org/W1998401374","https://openalex.org/W2007709253","https://openalex.org/W2022265565","https://openalex.org/W2039586696","https://openalex.org/W2043097947","https://openalex.org/W2050514626","https://openalex.org/W2051979333","https://openalex.org/W2058270372","https://openalex.org/W2077222540","https://openalex.org/W2096966061","https://openalex.org/W2497061289","https://openalex.org/W4230357017","https://openalex.org/W4243276261","https://openalex.org/W4246276228"],"related_works":["https://openalex.org/W2963352210","https://openalex.org/W1708834020","https://openalex.org/W4301805170","https://openalex.org/W2562682806","https://openalex.org/W2530602655","https://openalex.org/W2100237193","https://openalex.org/W1964416083","https://openalex.org/W2342167879","https://openalex.org/W2944466688","https://openalex.org/W2022813859"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,37],"multiplicity":[3],"of":[4,7,25,28,39],"periodic":[5,41],"solutions":[6],"nonautonomous":[8],"delay":[9],"differential":[10],"equations":[11],"which":[12],"are":[13,33],"asymptotically":[14],"linear":[15],"both":[16],"at":[17,20],"zero":[18],"and":[19],"infinity.":[21],"By":[22],"making":[23],"use":[24],"a":[26],"theorem":[27],"Benci,":[29],"some":[30],"sufficient":[31],"conditions":[32],"obtained":[34],"to":[35],"guarantee":[36],"existence":[38],"multiple":[40],"solutions.":[42]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
