{"id":"https://openalex.org/W2018889265","doi":"https://doi.org/10.1090/s0002-9939-1993-1154244-0","title":"Kamenev Type Theorems for Second Order Matrix Differential Systems","display_name":"Kamenev Type Theorems for Second Order Matrix Differential Systems","publication_year":1993,"publication_date":"1993-04-01","ids":{"openalex":"https://openalex.org/W2018889265","doi":"https://doi.org/10.1090/s0002-9939-1993-1154244-0","mag":"2018889265"},"language":"en","primary_location":{"id":"doi:10.1090/s0002-9939-1993-1154244-0","doi":"https://doi.org/10.1090/s0002-9939-1993-1154244-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9939-1993-1154244-0","pdf_url":"https://www.ams.org/proc/1993-117-04/S0002-9939-1993-1154244-0/S0002-9939-1993-1154244-0.pdf","source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/proc/1993-117-04/S0002-9939-1993-1154244-0/S0002-9939-1993-1154244-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018703593","display_name":"Lynn Erbe","orcid":"https://orcid.org/0000-0002-9644-0160","observed_orcids":["https://orcid.org/0000-0002-9644-0160"]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Lynn H. Erbe","raw_affiliation_strings":["Department of Mathematics , University of Alberta , Edmonton , Alberta , Canada T6G 2G1","University of Alberta"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Alberta , Edmonton , Alberta , Canada T6G 2G1","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"University of Alberta","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102892982","display_name":"Qingkai Kong","orcid":"https://orcid.org/0000-0003-1387-5896","observed_orcids":["https://orcid.org/0000-0003-1387-5896"]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Qingkai Kong","raw_affiliation_strings":["Department of Mathematics , University of Alberta , Edmonton , Alberta , Canada T6G 2G1","University of Alberta"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Alberta , Edmonton , Alberta , Canada T6G 2G1","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"University of Alberta","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111637753","display_name":"Shi Gui Ruan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Shi Gui Ruan","raw_affiliation_strings":["Department of Mathematics , University of Alberta , Edmonton , Alberta , Canada T6G 2G1","University of Alberta"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Alberta , Edmonton , Alberta , Canada T6G 2G1","institution_ids":["https://openalex.org/I154425047"]},{"raw_affiliation_string":"University of Alberta","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I154425047"],"apc_list":null,"apc_paid":null,"fwci":0.527,"has_fulltext":true,"cited_by_count":70,"citation_normalized_percentile":{"value":0.61606496,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"117","issue":"4","first_page":"957","last_page":"957"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9970999956130981,"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":0.9970999956130981,"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":0.0008999999845400453,"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"}},{"id":"https://openalex.org/T12812","display_name":"Meromorphic and Entire Functions","score":0.0006000000284984708,"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/oscillation-of-solutions","display_name":"oscillation of solutions","score":0.6930000185966492}],"concepts":[{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6739482283592224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6112618446350098},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5623588562011719},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.536849319934845},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5348803997039795},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4118877947330475},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40908384323120117},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39853742718696594},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08102384209632874},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.047015994787216187},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0002-9939-1993-1154244-0","doi":"https://doi.org/10.1090/s0002-9939-1993-1154244-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9939-1993-1154244-0","pdf_url":"https://www.ams.org/proc/1993-117-04/S0002-9939-1993-1154244-0/S0002-9939-1993-1154244-0.pdf","source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"},{"id":"doi:10.2307/2159522","doi":"https://doi.org/10.2307/2159522","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2159522","pdf_url":null,"source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0002-9939-1993-1154244-0","doi":"https://doi.org/10.1090/s0002-9939-1993-1154244-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0002-9939-1993-1154244-0","pdf_url":"https://www.ams.org/proc/1993-117-04/S0002-9939-1993-1154244-0/S0002-9939-1993-1154244-0.pdf","source":{"id":"https://openalex.org/S4210226894","display_name":"Proceedings of the American Mathematical Society","issn_l":"0002-9939","issn":["0002-9939","1088-6826"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the American Mathematical Society","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2018889265.pdf","grobid_xml":"https://content.openalex.org/works/W2018889265.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1967220550","https://openalex.org/W1974228823","https://openalex.org/W1976642059","https://openalex.org/W1977136522","https://openalex.org/W1995366946","https://openalex.org/W2003340587","https://openalex.org/W2006366814","https://openalex.org/W2024632086","https://openalex.org/W2028415557","https://openalex.org/W2030031620","https://openalex.org/W2039898578","https://openalex.org/W2055699032","https://openalex.org/W2057343462","https://openalex.org/W2058771063","https://openalex.org/W2085502604","https://openalex.org/W2085726618","https://openalex.org/W2091835816","https://openalex.org/W2315473342","https://openalex.org/W2328017031","https://openalex.org/W2565549492","https://openalex.org/W3021722416","https://openalex.org/W3141151088","https://openalex.org/W3143134995"],"related_works":["https://openalex.org/W2081858177","https://openalex.org/W1487459998","https://openalex.org/W1993809440","https://openalex.org/W2790541162","https://openalex.org/W1992507485","https://openalex.org/W2765238915","https://openalex.org/W2024632086","https://openalex.org/W2386700459","https://openalex.org/W2041244185","https://openalex.org/W2085726618"],"abstract_inverted_index":{"We":[0,49],"consider":[1],"the":[2,79],"second":[3],"order":[4,54],"matrix":[5,31],"differential":[6],"systems":[7],"(1)":[8,61],"$(P(t)Y\u2019)\u2019":[9],"+":[10,17],"Q(t)Y":[11,18],"=":[12,19],"0$":[13,20],"and":[14,23,36,62],"(2)":[15,63],"$Y''":[16],"where":[21],"$Y,\\;P$":[22],"$Q$":[24],"are":[25,64],"$n":[26],"\\times":[27],"n$":[28],"real":[29],"continuous":[30],"functions":[32],"with":[33],"$P(t),\\;Q(t)$":[34],"symmetric":[35],"$P(t)$":[37],"positive":[38],"definite":[39],"for":[40],"$t":[41],"\\in":[42],"[{t_0},\\infty":[43],")\\;(P(t)":[44],">":[45],"0,t":[46],"\\geqslant":[47],"{t_0})$.":[48],"establish":[50],"sufficient":[51],"conditions":[52],"in":[53,78],"that":[55],"all":[56],"prepared":[57],"solutions":[58],"$Y(t)$":[59],"of":[60,76],"oscillatory.":[65],"The":[66],"results":[67,75],"obtained":[68],"can":[69],"be":[70],"regarded":[71],"as":[72],"generalizing":[73],"well-known":[74],"Kamenev":[77],"scalar":[80],"case.":[81]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2016-06-24T00:00:00"}
