{"id":"https://openalex.org/W2065121571","doi":"https://doi.org/10.1155/2014/592513","title":"Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse","display_name":"Positive Periodic Solution for the Generalized Neutral Differential Equation with Multiple Delays and Impulse","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2065121571","doi":"https://doi.org/10.1155/2014/592513","mag":"2065121571"},"language":"en","primary_location":{"id":"doi:10.1155/2014/592513","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/592513","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/592513.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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"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/2014/592513.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074730600","display_name":"Zhenguo Luo","orcid":"https://orcid.org/0000-0002-3500-7152"},"institutions":[{"id":"https://openalex.org/I149735164","display_name":"Hengyang Normal University","ror":"https://ror.org/006bvjm48","country_code":"CN","type":"education","lineage":["https://openalex.org/I149735164"]},{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhenguo Luo","raw_affiliation_strings":["Department of Mathematics, Hengyang Normal University, Hengyang 421008, China","Department of Mathematics, National University of Defense Technology, Changsha 410073, China"],"raw_orcid":"https://orcid.org/0000-0002-3500-7152","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hengyang Normal University, Hengyang 421008, China","institution_ids":["https://openalex.org/I149735164"]},{"raw_affiliation_string":"Department of Mathematics, National University of Defense Technology, Changsha 410073, China","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109852087","display_name":"Liping Luo","orcid":null},"institutions":[{"id":"https://openalex.org/I149735164","display_name":"Hengyang Normal University","ror":"https://ror.org/006bvjm48","country_code":"CN","type":"education","lineage":["https://openalex.org/I149735164"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liping Luo","raw_affiliation_strings":["Department of Mathematics, Hengyang Normal University, Hengyang 421008, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hengyang Normal University, Hengyang 421008, China","institution_ids":["https://openalex.org/I149735164"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048975990","display_name":"Yunhui Zeng","orcid":"https://orcid.org/0000-0002-7672-9768"},"institutions":[{"id":"https://openalex.org/I149735164","display_name":"Hengyang Normal University","ror":"https://ror.org/006bvjm48","country_code":"CN","type":"education","lineage":["https://openalex.org/I149735164"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunhui Zeng","raw_affiliation_strings":["Department of Mathematics, Hengyang Normal University, Hengyang 421008, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hengyang Normal University, Hengyang 421008, China","institution_ids":["https://openalex.org/I149735164"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074730600"],"corresponding_institution_ids":["https://openalex.org/I149735164","https://openalex.org/I170215575"],"apc_list":{"value":1130,"currency":"USD","value_usd":1130},"apc_paid":{"value":1130,"currency":"USD","value_usd":1130},"fwci":0.4319,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6248047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9988999962806702,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9988999962806702,"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":0.9923999905586243,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.991100013256073,"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/algorithm","display_name":"Algorithm","score":0.44644051790237427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21670907735824585}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.44644051790237427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21670907735824585}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/592513","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/592513","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/592513.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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"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/1425305566","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425305566","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:592513","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/592513.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:62a77299b1904ec6b06daff22e8952b2","is_oa":true,"landing_page_url":"https://doaj.org/article/62a77299b1904ec6b06daff22e8952b2","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 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/592513","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/592513","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/592513.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","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"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/G1280167330","display_name":null,"funder_award_id":"10971229","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G150648515","display_name":null,"funder_award_id":"13JJ4098","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1922592740","display_name":null,"funder_award_id":"12JJ9001","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G2197447244","display_name":null,"funder_award_id":"10971229","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G2238063630","display_name":null,"funder_award_id":"12C0541","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G2266907518","display_name":null,"funder_award_id":"11371367","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G2998248796","display_name":null,"funder_award_id":"11371367","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G3043958933","display_name":null,"funder_award_id":"13C084","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G3179747805","display_name":null,"funder_award_id":"2013T60934","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G3268597577","display_name":null,"funder_award_id":"12C0361","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3362956981","display_name":"\u8109\u51b2\u5fae\u5206\u65b9\u7a0b\u7684\u5468\u671f\u89e3\u53ca\u5176\u76f8\u5173\u95ee\u9898\u7684\u7814\u7a76","funder_award_id":"10971229","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3502565120","display_name":null,"funder_award_id":"13JJ4098","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G4012641011","display_name":null,"funder_award_id":"12C0541","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4025733381","display_name":null,"funder_award_id":"2013T60934","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G414085153","display_name":null,"funder_award_id":"11161015","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G4203653553","display_name":null,"funder_award_id":"11JJ900","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G4342950568","display_name":null,"funder_award_id":"12C0541","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G4348818831","display_name":null,"funder_award_id":"13C084","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G4363692225","display_name":null,"funder_award_id":"11161015","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G4481548493","display_name":"\u975e\u9ad8\u65af\u566a\u58f0\u9a71\u52a8\u7684\u65e0\u7a77\u7ef4\u968f\u673a\u52a8\u529b\u7cfb\u7edf\u7684\u52a8\u529b\u5b66\u7814\u7a76","funder_award_id":"11371367","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4492806459","display_name":null,"funder_award_id":"12C0361","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G4667459869","display_name":null,"funder_award_id":"2012M512162","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G4821220673","display_name":null,"funder_award_id":"12C0361","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G5273820076","display_name":null,"funder_award_id":"11JJ900","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5306241130","display_name":null,"funder_award_id":"11JJ900","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6118962194","display_name":null,"funder_award_id":"11371367","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6368373558","display_name":"\u591a\u56e0\u7d20\u5f71\u54cd\u5fae\u5206\u7cfb\u7edf\u5b9a\u6027\u7814\u7a76\u4e0e\u4eff\u771f\u5206\u6790","funder_award_id":"11161015","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6739567429","display_name":null,"funder_award_id":"2012M512162","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G675757661","display_name":null,"funder_award_id":"2012M512162","funder_id":"https://openalex.org/F4320334992","funder_display_name":"Construct Program of the Key Discipline in Hunan Province"},{"id":"https://openalex.org/G7321604585","display_name":null,"funder_award_id":"2013T60934","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G7639987013","display_name":null,"funder_award_id":"13JJ4098","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G768509702","display_name":null,"funder_award_id":"12JJ9001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7784457621","display_name":null,"funder_award_id":"12JJ9001","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G8177466589","display_name":null,"funder_award_id":"13C084","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320334992","display_name":"Construct Program of the Key Discipline in Hunan Province","ror":"https://ror.org/00xsfaz62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2065121571.pdf","grobid_xml":"https://content.openalex.org/works/W2065121571.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W580296679","https://openalex.org/W1586658033","https://openalex.org/W1969109726","https://openalex.org/W1986888616","https://openalex.org/W1993672075","https://openalex.org/W1999304834","https://openalex.org/W2005007615","https://openalex.org/W2006773209","https://openalex.org/W2007581253","https://openalex.org/W2014432434","https://openalex.org/W2033572723","https://openalex.org/W2054724195","https://openalex.org/W2057152735","https://openalex.org/W2068868978","https://openalex.org/W2071396093","https://openalex.org/W2168394909","https://openalex.org/W4205909971"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2052122378","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"By":[0],"using":[1],"a":[2],"fixed":[3],"point":[4],"theorem":[5,16],"of":[6,33,37,56],"strict-set-contraction,":[7],"which":[8],"is":[9],"different":[10],"from":[11],"Gaines":[12],"and":[13,17,68],"Mawhin's":[14],"continuation":[15,19],"abstract":[18],"theory":[20],"for":[21,30],"k":[22],"-set":[23],"contraction,":[24],"we":[25,59],"established":[26],"some":[27,62],"new":[28,69],"criteria":[29],"the":[31,38],"existence":[32],"positive":[34],"periodic":[35],"solution":[36],"following":[39],"generalized":[40],"neutral":[41],"delay":[42],"functional":[43],"differential":[44],"equation":[45],"with":[46],"impulse:":[47],"x'(t)=x(t)[a(t)-f(t,x(t),x(t-\u03c41(t,x(t))),\u2026,x(t-\u03c4n(t,x(t))),x'(t-\u03b31(t,x(t))),\u2026,x'(t-\u03b3m(t,x(t))))],":[48],"t\u2260tk,":[49],"k\u2208Z+;":[50],"x(tk+)=x(tk-)+\u03b8k(x(tk)),":[51],"k\u2208Z+":[52],".":[53],"As":[54],"applications":[55,63],"our":[57],"results,":[58],"also":[60],"give":[61],"to":[64],"several":[65],"Lotka-Volterra":[66],"models":[67],"results":[70],"are":[71],"obtained.":[72]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}