{"id":"https://openalex.org/W2002169119","doi":"https://doi.org/10.1134/s0012266108100029","title":"On the sequences of zeros of holomorphic solutions of linear second-order differential equations","display_name":"On the sequences of zeros of holomorphic solutions of linear second-order differential equations","publication_year":2008,"publication_date":"2008-10-01","ids":{"openalex":"https://openalex.org/W2002169119","doi":"https://doi.org/10.1134/s0012266108100029","mag":"2002169119"},"language":"en","primary_location":{"id":"doi:10.1134/s0012266108100029","doi":"https://doi.org/10.1134/s0012266108100029","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0012266108100029","pdf_url":null,"source":{"id":"https://openalex.org/S71958379","display_name":"Differential Equations","issn_l":"0012-2661","issn":["0012-2661","1608-3083"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Differential Equations","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018506535","display_name":"Bogdan Vasil'evich Vinnitskii","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210151083","display_name":"Drohobych Ivan Franko State Pedagogical University","ror":"https://ror.org/04vpyax58","country_code":"UA","type":"education","lineage":["https://openalex.org/I4210151083"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"B. V. Vinnitskii","raw_affiliation_strings":["Drogobych State Pedagogical University, Drogobych, Ukraine","Drogobych State Pedagogical University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Drogobych State Pedagogical University, Drogobych, Ukraine","institution_ids":["https://openalex.org/I4210151083"]},{"raw_affiliation_string":"Drogobych State Pedagogical University","institution_ids":["https://openalex.org/I4210151083"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078330948","display_name":"O. V. Shavala","orcid":"https://orcid.org/0000-0003-1061-3807","observed_orcids":["https://orcid.org/0000-0003-1061-3807"]},"institutions":[{"id":"https://openalex.org/I4210151083","display_name":"Drohobych Ivan Franko State Pedagogical University","ror":"https://ror.org/04vpyax58","country_code":"UA","type":"education","lineage":["https://openalex.org/I4210151083"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"E. V. Shavala","raw_affiliation_strings":["Drogobych State Pedagogical University, Drogobych, Ukraine","Drogobych State Pedagogical University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Drogobych State Pedagogical University, Drogobych, Ukraine","institution_ids":["https://openalex.org/I4210151083"]},{"raw_affiliation_string":"Drogobych State Pedagogical University","institution_ids":["https://openalex.org/I4210151083"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210151083"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.10286817,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"44","issue":"10","first_page":"1361","last_page":"1366"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12812","display_name":"Meromorphic and Entire Functions","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/T12812","display_name":"Meromorphic and Entire Functions","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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.00039999998989515007,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/second-order-linear-differential-equations","display_name":"second-order linear differential equations","score":0.9229999780654907},{"id":"https://openalex.org/keywords/meromorphic-coefficients","display_name":"meromorphic coefficients","score":0.9430000185966492},{"id":"https://openalex.org/keywords/second-order-poles","display_name":"second-order poles","score":0.8939999938011169},{"id":"https://openalex.org/keywords/meromorphic-solutions","display_name":"meromorphic solutions","score":0.8740000128746033},{"id":"https://openalex.org/keywords/nevanlinna-theory","display_name":"Nevanlinna theory","score":0.7760000228881836},{"id":"https://openalex.org/keywords/necessary-and-sufficient-conditions","display_name":"necessary and sufficient conditions","score":0.6399999856948853}],"concepts":[{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.9404560923576355},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.9106311202049255},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8739186525344849},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.6887316107749939},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6593113541603088},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5970802903175354},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5860819816589355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.503985583782196},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.48649924993515015},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.47233739495277405},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3759456276893616},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0012266108100029","doi":"https://doi.org/10.1134/s0012266108100029","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0012266108100029","pdf_url":null,"source":{"id":"https://openalex.org/S71958379","display_name":"Differential Equations","issn_l":"0012-2661","issn":["0012-2661","1608-3083"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Differential Equations","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1530798444","https://openalex.org/W1545068088","https://openalex.org/W1555941985","https://openalex.org/W1787323876","https://openalex.org/W2162277793","https://openalex.org/W2991644655","https://openalex.org/W2994685737","https://openalex.org/W4237989679"],"related_works":["https://openalex.org/W2032758607","https://openalex.org/W2032118454","https://openalex.org/W2800672890","https://openalex.org/W2036332869","https://openalex.org/W2383099095","https://openalex.org/W250235855","https://openalex.org/W7220602866","https://openalex.org/W2056979140","https://openalex.org/W2351217323","https://openalex.org/W2358037273"],"abstract_inverted_index":{"We":[0],"find":[1],"necessary":[2],"and":[3],"sufficient":[4],"conditions":[5],"under":[6],"which":[7],"a":[8,22,32,38,41,51],"finite":[9],"or":[10],"infinite":[11],"sequence":[12,18],"of":[13,19,21,25,56],"complex":[14],"numbers":[15],"is":[16],"the":[17,26],"zeros":[20],"holomorphic":[23],"solution":[24],"linear":[27,58],"differential":[28],"equation":[29],"f\u2033":[30],"+":[31],"0":[33,36,42],"f":[34],"=":[35],"with":[37],"meromorphic":[39],"coefficient":[40],"that":[43],"has":[44],"second-order":[45,57],"poles.":[46],"In":[47],"addition,":[48],"we":[49],"present":[50],"criterion":[52],"for":[53],"all":[54],"solutions":[55],"equations":[59],"to":[60],"be":[61],"meromorphic.":[62]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-09-22T06:50:58.402377","created_date":"2016-06-24T00:00:00"}