{"id":"https://openalex.org/W2069448126","doi":"https://doi.org/10.1155/2011/262316","title":"Convergence and Divergence of the Solutions of a Neutral Difference Equation","display_name":"Convergence and Divergence of the Solutions of a Neutral Difference Equation","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2069448126","doi":"https://doi.org/10.1155/2011/262316","mag":"2069448126"},"language":"en","primary_location":{"id":"doi:10.1155/2011/262316","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/262316","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/262316.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/2011/262316.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014915773","display_name":"George E. Chatzarakis","orcid":"https://orcid.org/0000-0002-0477-1895"},"institutions":[{"id":"https://openalex.org/I254421610","display_name":"School of Pedagogical and Technological Education","ror":"https://ror.org/04v3r9z94","country_code":"GR","type":"education","lineage":["https://openalex.org/I254421610"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"G. E. Chatzarakis","raw_affiliation_strings":["Department of Electrical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklion, 14121 Athens, Greece aspete.gr","Department of Electrical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklion, 14121 Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklion, 14121 Athens, Greece aspete.gr","institution_ids":["https://openalex.org/I254421610"]},{"raw_affiliation_string":"Department of Electrical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklion, 14121 Athens, Greece","institution_ids":["https://openalex.org/I254421610"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028182788","display_name":"G. N. Miliaras","orcid":null},"institutions":[{"id":"https://openalex.org/I254421610","display_name":"School of Pedagogical and Technological Education","ror":"https://ror.org/04v3r9z94","country_code":"GR","type":"education","lineage":["https://openalex.org/I254421610"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"G. N. Miliaras","raw_affiliation_strings":["Department of Electrical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklion, 14121 Athens, Greece aspete.gr","Department of Electrical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklion, 14121 Athens, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklion, 14121 Athens, Greece aspete.gr","institution_ids":["https://openalex.org/I254421610"]},{"raw_affiliation_string":"Department of Electrical Engineering Educators, School of Pedagogical and Technological Education (ASPETE), N. Heraklion, 14121 Athens, Greece","institution_ids":["https://openalex.org/I254421610"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014915773"],"corresponding_institution_ids":["https://openalex.org/I254421610"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":1.937,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84142004,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9984999895095825,"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":0.9984999895095825,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9973999857902527,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8030783534049988},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.725263237953186},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.6985596418380737},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.618281364440918},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6141533255577087},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5910777449607849},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5279924869537354},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4833921492099762},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4695088565349579},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44072407484054565},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40726688504219055}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8030783534049988},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.725263237953186},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.6985596418380737},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.618281364440918},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6141533255577087},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5910777449607849},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5279924869537354},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4833921492099762},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4695088565349579},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44072407484054565},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40726688504219055},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2011/262316","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/262316","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/262316.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/1331818651","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1331818651","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:262316","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2011/262316.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:a6f70db716b44b16a4efc53e090cd98e","is_oa":true,"landing_page_url":"https://doaj.org/article/a6f70db716b44b16a4efc53e090cd98e","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:10.1155/2011/262316","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/262316","pdf_url":"https://downloads.hindawi.com/journals/jam/2011/262316.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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.550000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2069448126.pdf","grobid_xml":"https://content.openalex.org/works/W2069448126.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W54190265","https://openalex.org/W134346268","https://openalex.org/W196597558","https://openalex.org/W639417630","https://openalex.org/W639834748","https://openalex.org/W814244611","https://openalex.org/W1504808036","https://openalex.org/W1506680237","https://openalex.org/W1967194864","https://openalex.org/W1971690820","https://openalex.org/W1973553707","https://openalex.org/W1974587197","https://openalex.org/W1974977543","https://openalex.org/W1978092051","https://openalex.org/W1990746352","https://openalex.org/W1991654791","https://openalex.org/W1994103904","https://openalex.org/W2001961465","https://openalex.org/W2008727563","https://openalex.org/W2014172170","https://openalex.org/W2014969630","https://openalex.org/W2016654505","https://openalex.org/W2028677131","https://openalex.org/W2035248164","https://openalex.org/W2037727161","https://openalex.org/W2038277270","https://openalex.org/W2040433724","https://openalex.org/W2050960148","https://openalex.org/W2055205829","https://openalex.org/W2059082897","https://openalex.org/W2066136768","https://openalex.org/W2071871248","https://openalex.org/W2072933133","https://openalex.org/W2076987593","https://openalex.org/W2077579732","https://openalex.org/W2079871064","https://openalex.org/W2088355206","https://openalex.org/W2093168672","https://openalex.org/W2132421705","https://openalex.org/W2137795015","https://openalex.org/W2142396193","https://openalex.org/W2142763779","https://openalex.org/W2188418168","https://openalex.org/W2313139201","https://openalex.org/W2323813375","https://openalex.org/W2735318481","https://openalex.org/W4231677858","https://openalex.org/W4293087381","https://openalex.org/W6623286001","https://openalex.org/W6687138121"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W1980454230","https://openalex.org/W2300851791","https://openalex.org/W2340858455"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,6,15,100,123,127],"asymptotic":[3,124],"behavior":[4,125],"of":[5,8,14,79,126],"solutions":[7,128],"a":[9,49,58,77],"neutral":[10],"type":[11],"difference":[12,102],"equation":[13],"form":[16],"\u0394[":[17],"x":[18,24,35,105,110,116],"(":[19,25,27,32,36,38,45,54,69,71,86,106,111,117],"n":[20,28,33,39,46,55,72,74,87,107,112,118],")":[21,34,47,56,88,108],"+":[22,30,95,113],"c":[23,65,139],"\u03c4":[26,44],"))]":[29],"p":[31,70,85,90,92],"\u03c3":[37,53],"))":[40,73],"=":[41,109],"0,":[42],"where":[43],"is":[48,57,76],"general":[50,59],"retarded":[51],"argument,":[52],"deviated":[60],"argument":[61],"(retarded":[62],"or":[63],"advanced),":[64],"\u2208":[66,93],"\u211d":[67,94],",":[68,91,96],"\u22650":[75],"sequence":[78],"positive":[80],"real":[81],"numbers":[82],"such":[83],"that":[84],"\u2265":[89],"and":[97,134],"\u0394":[98,104],"denotes":[99],"forward":[101],"operator":[103],"1)":[114],"\u2212":[115],").":[119],"Also,":[120],"we":[121],"examine":[122],"in":[129],"case":[130],"they":[131],"are":[132],"continuous":[133],"differentiable":[135],"with":[136],"respect":[137],"to":[138],".":[140]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}