{"id":"https://openalex.org/W3088869982","doi":"https://doi.org/10.1142/s0218127420501588","title":"Periodic Solutions of Continuous Third-Order Differential Equations with Piecewise Polynomial Nonlinearities","display_name":"Periodic Solutions of Continuous Third-Order Differential Equations with Piecewise Polynomial Nonlinearities","publication_year":2020,"publication_date":"2020-09-15","ids":{"openalex":"https://openalex.org/W3088869982","doi":"https://doi.org/10.1142/s0218127420501588","mag":"3088869982"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420501588","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420501588","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ddd.uab.cat/record/236654","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046015548","display_name":"Jaume Llibre","orcid":"https://orcid.org/0000-0002-9511-5999"},"institutions":[{"id":"https://openalex.org/I123044942","display_name":"Universitat Aut\u00f2noma de Barcelona","ror":"https://ror.org/052g8jq94","country_code":"ES","type":"education","lineage":["https://openalex.org/I123044942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"J. Llibre","raw_affiliation_strings":["Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain","institution_ids":["https://openalex.org/I123044942"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048713246","display_name":"Bruno D. Lopes","orcid":null},"institutions":[{"id":"https://openalex.org/I71715416","display_name":"Universidade Federal do ABC","ror":"https://ror.org/028kg9j04","country_code":"BR","type":"education","lineage":["https://openalex.org/I71715416"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"B. D. Lopes","raw_affiliation_strings":["Centro de Matem\u00e1tica, Computa\u00e7\u00e3o e Cogni\u00e7\u00e3o, Universidade Federal do ABC, 09210\u2013170, Santo Andr\u00e9, S\u00e3o Paulo, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Matem\u00e1tica, Computa\u00e7\u00e3o e Cogni\u00e7\u00e3o, Universidade Federal do ABC, 09210\u2013170, Santo Andr\u00e9, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I71715416"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070929617","display_name":"Jaime R. de Moraes","orcid":"https://orcid.org/0000-0002-7722-6644"},"institutions":[{"id":"https://openalex.org/I2802295813","display_name":"Universidade Estadual de Mato Grosso do Sul","ror":"https://ror.org/02ggt9460","country_code":"BR","type":"education","lineage":["https://openalex.org/I2802295813"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"J. R. de Moraes","raw_affiliation_strings":["Curso de Matem\u00e1tica, Universidade Estadual de Mato Grosso do Sul, 79804\u2013970, Dourados, Mato Grosso do Sul, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-7722-6644","affiliations":[{"raw_affiliation_string":"Curso de Matem\u00e1tica, Universidade Estadual de Mato Grosso do Sul, 79804\u2013970, Dourados, Mato Grosso do Sul, Brazil","institution_ids":["https://openalex.org/I2802295813"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5046015548"],"corresponding_institution_ids":["https://openalex.org/I123044942"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.21597796,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"30","issue":"11","first_page":"2050158","last_page":"2050158"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9976999759674072,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7670388221740723},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7611702680587769},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5847721099853516},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5002856254577637},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49496573209762573},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.492376446723938},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4841764271259308},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.44500941038131714},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.439363956451416},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.419694185256958},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.4125218391418457},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11553263664245605},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.101093590259552}],"concepts":[{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7670388221740723},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7611702680587769},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5847721099853516},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5002856254577637},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49496573209762573},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.492376446723938},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4841764271259308},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.44500941038131714},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.439363956451416},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.419694185256958},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.4125218391418457},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11553263664245605},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.101093590259552},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218127420501588","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127420501588","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},{"id":"pmh:oai:ddd.uab.cat:236654","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/236654","pdf_url":null,"source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:236654","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/236654","pdf_url":null,"source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"host_organization_lineage_names":[],"type":"repository"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1972054749","https://openalex.org/W1995830660","https://openalex.org/W2008423115","https://openalex.org/W2019143828","https://openalex.org/W2030496841","https://openalex.org/W2120749007","https://openalex.org/W2139794367","https://openalex.org/W2173982901","https://openalex.org/W2185115942","https://openalex.org/W2230515575","https://openalex.org/W2464837953","https://openalex.org/W2521317762","https://openalex.org/W2532001266"],"related_works":["https://openalex.org/W2383844134","https://openalex.org/W3093305317","https://openalex.org/W2374198922","https://openalex.org/W2889599571","https://openalex.org/W1833822726","https://openalex.org/W2798137860","https://openalex.org/W2065958989","https://openalex.org/W2048650277","https://openalex.org/W1998603635","https://openalex.org/W2363810458"],"abstract_inverted_index":{"We":[0,35],"consider":[1],"third-order":[2],"autonomous":[3],"continuous":[4,44],"piecewise":[5],"differential":[6,16,40,58],"equations":[7,17],"in":[8],"the":[9,21,32,39,50,57],"variable":[10],"[Formula:":[11,23,65],"see":[12,24,66],"text].":[13,67],"For":[14],"such":[15],"with":[18],"nonlinearities":[19],"of":[20,63],"form":[22],"text],":[25],"we":[26,45],"investigate":[27],"their":[28],"periodic":[29],"solutions":[30],"using":[31],"averaging":[33,52],"theory.":[34],"remark":[36],"that":[37,54,56],"since":[38],"system":[41,59],"is":[42],"only":[43],"cannot":[46],"apply":[47],"to":[48],"it":[49],"classical":[51],"theory,":[53],"needs":[55],"be":[60],"at":[61],"least":[62],"class":[64]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
