{"id":"https://openalex.org/W2982053771","doi":"https://doi.org/10.3390/sym11111332","title":"A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay","display_name":"A Sharp Oscillation Criterion for a Linear Differential Equation with Variable Delay","publication_year":2019,"publication_date":"2019-10-24","ids":{"openalex":"https://openalex.org/W2982053771","doi":"https://doi.org/10.3390/sym11111332","mag":"2982053771"},"language":"en","primary_location":{"id":"doi:10.3390/sym11111332","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11111332","pdf_url":"https://www.mdpi.com/2073-8994/11/11/1332/pdf","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/2073-8994/11/11/1332/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081568805","display_name":"\u00c1bel Garab","orcid":"https://orcid.org/0000-0001-9693-1923"},"institutions":[{"id":"https://openalex.org/I4210166741","display_name":"University of Klagenfurt","ror":"https://ror.org/05q9m0937","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210166741"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"\u00c1bel Garab","raw_affiliation_strings":["Institute of Mathematics, University of Klagenfurt, Universit\u00e4tsstra\u00dfe 65\u201367, 9020 Klagenfurt am W\u00f6rthersee, Austria"],"raw_orcid":"https://orcid.org/0000-0001-9693-1923","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of Klagenfurt, Universit\u00e4tsstra\u00dfe 65\u201367, 9020 Klagenfurt am W\u00f6rthersee, Austria","institution_ids":["https://openalex.org/I4210166741"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081568805"],"corresponding_institution_ids":["https://openalex.org/I4210166741"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.8033,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.91111008,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"11","issue":"11","first_page":"1332","last_page":"1332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.996999979019165,"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":0.996999979019165,"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":0.996999979019165,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.721367597579956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6113635897636414},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.5798318982124329},{"id":"https://openalex.org/keywords/functional-differential-equation","display_name":"Functional differential equation","score":0.5730975270271301},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5725199580192566},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5393528938293457},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.532407820224762},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5039195418357849},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4781452417373657},{"id":"https://openalex.org/keywords/linear-differential-equation","display_name":"Linear differential equation","score":0.4461880922317505},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3644828200340271},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35075926780700684}],"concepts":[{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.721367597579956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6113635897636414},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.5798318982124329},{"id":"https://openalex.org/C2778025262","wikidata":"https://www.wikidata.org/wiki/Q28406324","display_name":"Functional differential equation","level":3,"score":0.5730975270271301},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5725199580192566},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5393528938293457},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.532407820224762},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5039195418357849},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4781452417373657},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.4461880922317505},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3644828200340271},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35075926780700684},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11111332","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11111332","pdf_url":"https://www.mdpi.com/2073-8994/11/11/1332/pdf","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:0d6e2b6943ce40c6840ac607608a260c","is_oa":true,"landing_page_url":"https://doaj.org/article/0d6e2b6943ce40c6840ac607608a260c","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 11, Iss 11, p 1332 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11111332","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11111332","pdf_url":"https://www.mdpi.com/2073-8994/11/11/1332/pdf","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W610742528","https://openalex.org/W627954411","https://openalex.org/W653547768","https://openalex.org/W1494118823","https://openalex.org/W1606251380","https://openalex.org/W2083862038","https://openalex.org/W2609676907","https://openalex.org/W2802398000","https://openalex.org/W2913587277","https://openalex.org/W4210960242","https://openalex.org/W4211202937","https://openalex.org/W4213373779","https://openalex.org/W4388215494"],"related_works":["https://openalex.org/W2390991069","https://openalex.org/W2348576774","https://openalex.org/W2362061707","https://openalex.org/W2150987529","https://openalex.org/W2352047463","https://openalex.org/W2386228494","https://openalex.org/W2073949697","https://openalex.org/W2356614427","https://openalex.org/W2347836400","https://openalex.org/W2068450643"],"abstract_inverted_index":{"We":[0],"consider":[1],"linear":[2],"differential":[3,180],"equations":[4],"with":[5],"variable":[6],"delay":[7,179],"of":[8,93,176],"the":[9,91,145,177],"form":[10],"x":[11,21],"\u2032":[12],"(":[13,18,22,26,63,76,109,121,128,133],"t":[14,19,23,27,33,35,42,57,73,77,82,105,110,122,125,129,131],")":[15,20,28,29,46,52,61,67,78,111,123,130,135],"+":[16],"p":[17,39,132,162],"\u2212":[24,74,126],"\u03c4":[25,54,75,127,164],"=":[30,102,120],"0":[31,36,43,49,58,64],",":[32,37,44,50,59,65,116,165],"\u2265":[34,112],"where":[38,117],":":[40,55,101,119],"[":[41,48,56],"\u221e":[45,51,60,66,80,84,107],"\u2192":[47,62,79,83,106],"and":[53,163],"are":[68,182],"continuous":[69],"functions,":[70],"such":[71],"that":[72,99,173],"(as":[81],").":[85],"It":[86],"is":[87,97,148],"well-known":[88],"that,":[89,143],"for":[90],"oscillation":[92],"all":[94,174],"solutions,":[95],"it":[96],"necessary":[98],"B":[100,167],"lim":[103],"sup":[104],"A":[108,118,147],"1":[113,169],"e":[114,171],"holds":[115],"\u222b":[124],"s":[134,137],"d":[136],".":[138],"Our":[139],"main":[140],"result":[141],"shows":[142],"if":[144],"function":[146],"slowly":[149],"varying":[150],"at":[151],"infinity":[152],"(in":[153],"additive":[154],"form),":[155],"then":[156],"under":[157],"mild":[158],"additional":[159],"assumptions":[160],"on":[161],"condition":[166],">":[168],"/":[170],"implies":[172],"solutions":[175],"above":[178],"equation":[181],"oscillatory.":[183]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}