{"id":"https://openalex.org/W3133512768","doi":"https://doi.org/10.3390/sym13030449","title":"Monotone Iterative Technique for the Periodic Solutions of High-Order Delayed Differential Equations in Abstract Spaces","display_name":"Monotone Iterative Technique for the Periodic Solutions of High-Order Delayed Differential Equations in Abstract Spaces","publication_year":2021,"publication_date":"2021-03-10","ids":{"openalex":"https://openalex.org/W3133512768","doi":"https://doi.org/10.3390/sym13030449","mag":"3133512768"},"language":"en","primary_location":{"id":"doi:10.3390/sym13030449","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13030449","pdf_url":"https://www.mdpi.com/2073-8994/13/3/449/pdf?version=1615370045","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/2073-8994/13/3/449/pdf?version=1615370045","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012349590","display_name":"He Yang","orcid":"https://orcid.org/0000-0001-9273-1473"},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"He Yang","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China"],"raw_orcid":"https://orcid.org/0000-0001-9273-1473","affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China","institution_ids":["https://openalex.org/I68986083"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048682678","display_name":"Yongxiang Li","orcid":"https://orcid.org/0000-0002-5193-030X"},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongxiang Li","raw_affiliation_strings":["College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China"],"raw_orcid":"https://orcid.org/0000-0002-5193-030X","affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China","institution_ids":["https://openalex.org/I68986083"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5012349590"],"corresponding_institution_ids":["https://openalex.org/I68986083"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04702908,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"3","first_page":"449","last_page":"449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976000189781189,"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":0.9976000189781189,"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":0.9939000010490417,"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":0.9901000261306763,"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/uniqueness","display_name":"Uniqueness","score":0.8047101497650146},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.79566490650177},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7512168884277344},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7237993478775024},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6113482117652893},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5884681940078735},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4476626217365265},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.421073317527771},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4096635580062866},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4018184542655945},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34038370847702026},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3372992277145386},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3328099846839905},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0775471031665802},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.045383453369140625}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8047101497650146},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.79566490650177},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7512168884277344},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7237993478775024},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6113482117652893},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5884681940078735},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4476626217365265},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.421073317527771},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4096635580062866},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4018184542655945},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34038370847702026},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3372992277145386},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3328099846839905},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0775471031665802},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.045383453369140625},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13030449","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13030449","pdf_url":"https://www.mdpi.com/2073-8994/13/3/449/pdf?version=1615370045","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:04ed7d0aecde4825bada68362c9c17c6","is_oa":true,"landing_page_url":"https://doaj.org/article/04ed7d0aecde4825bada68362c9c17c6","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 13, Iss 3, p 449 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/3/449/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13030449","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/sym13030449","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13030449","pdf_url":"https://www.mdpi.com/2073-8994/13/3/449/pdf?version=1615370045","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3133512768.pdf"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W297981433","https://openalex.org/W1555674425","https://openalex.org/W1605250361","https://openalex.org/W1993714221","https://openalex.org/W2009962591","https://openalex.org/W2031715575","https://openalex.org/W2048498118","https://openalex.org/W2056709448","https://openalex.org/W2081707011","https://openalex.org/W2184787981","https://openalex.org/W7002144850"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W2903488900","https://openalex.org/W2074838282","https://openalex.org/W2043671984"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,33],"the":[4,40,48],"existence":[5,53],"of":[6,42],"\u03c9-periodic":[7,32],"solutions":[8,46],"for":[9],"nth-order":[10],"ordinary":[11],"differential":[12],"equation":[13],"involving":[14],"fixed":[15],"delay":[16],"in":[17],"Banach":[18],"space":[19],"E.":[20],"Lnu(t)=f(t,u(t),u(t\u2212\u03c4)),t\u2208R,":[21],"where":[22],"Lnu(t):=u(n)(t)+\u2211i=0n\u22121aiu(i)(t),":[23],"ai\u2208R,":[24],"i=0,1,\u22ef,n\u22121,":[25],"are":[26,57],"constants,":[27],"f(t,x,y):R\u00d7E\u00d7E\u27f6E":[28],"is":[29],"continuous":[30],"and":[31,44,47,54],"respect":[34],"to":[35],"t,":[36],"\u03c4>0.":[37],"By":[38],"applying":[39],"approach":[41],"upper":[43],"lower":[45],"monotone":[49],"iterative":[50],"technique,":[51],"some":[52],"uniqueness":[55],"theorems":[56],"proved":[58],"under":[59],"essential":[60],"conditions.":[61]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}