{"id":"https://openalex.org/W1995253776","doi":"https://doi.org/10.1016/0022-247x(74)90011-0","title":"On Liapunov functions for nonautonomous systems","display_name":"On Liapunov functions for nonautonomous systems","publication_year":1974,"publication_date":"1974-09-01","ids":{"openalex":"https://openalex.org/W1995253776","doi":"https://doi.org/10.1016/0022-247x(74)90011-0","mag":"1995253776"},"language":"en","primary_location":{"id":"doi:10.1016/0022-247x(74)90011-0","doi":"https://doi.org/10.1016/0022-247x(74)90011-0","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0022-247x(74)90011-0","pdf_url":"https://www.sciencedirect.com/science/article/pii/0022247X74900110/pdf","source":{"id":"https://openalex.org/S151579836","display_name":"Journal of Mathematical Analysis and Applications","issn_l":"0022-247X","issn":["0022-247X","1096-0813"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Analysis and Applications","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.sciencedirect.com/science/article/pii/0022247X74900110/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081236257","display_name":"John R. Haddock","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John R Haddock","raw_affiliation_strings":["Memphis State University, Memphis, Tennessee 38152, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Memphis State University, Memphis, Tennessee 38152, USA","institution_ids":["https://openalex.org/I94658018"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5081236257"],"corresponding_institution_ids":["https://openalex.org/I94658018"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":1.625,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.8490818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"47","issue":"3","first_page":"599","last_page":"603"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.33149999380111694,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.33149999380111694,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.31349998712539673,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.21799999475479126,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.9359999895095825},{"id":"https://openalex.org/keywords/non-autonomous-systems","display_name":"non-autonomous systems","score":0.9390000104904175},{"id":"https://openalex.org/keywords/limit-sets","display_name":"limit sets","score":0.8560000061988831},{"id":"https://openalex.org/keywords/lasalle-s-invariance-principle","display_name":"LaSalle invariance principle","score":0.8320000171661377},{"id":"https://openalex.org/keywords/stability-theory","display_name":"stability theory","score":0.4659999907016754},{"id":"https://openalex.org/keywords/systems-of-differential-equations","display_name":"systems of differential equations","score":0.7860000133514404},{"id":"https://openalex.org/keywords/asymptotic-behavior-of-solutions","display_name":"asymptotic behavior of solutions","score":0.7210000157356262}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9084863662719727},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.8051667213439941},{"id":"https://openalex.org/C2988193574","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Liapunov function","level":3,"score":0.7615646123886108},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.47947248816490173},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44779253005981445},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43971046805381775},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42520871758461},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4237765669822693},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41056957840919495},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3699815273284912},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11711063981056213},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0022-247x(74)90011-0","doi":"https://doi.org/10.1016/0022-247x(74)90011-0","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0022-247x(74)90011-0","pdf_url":"https://www.sciencedirect.com/science/article/pii/0022247X74900110/pdf","source":{"id":"https://openalex.org/S151579836","display_name":"Journal of Mathematical Analysis and Applications","issn_l":"0022-247X","issn":["0022-247X","1096-0813"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Analysis and Applications","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/0022-247x(74)90011-0","doi":"https://doi.org/10.1016/0022-247x(74)90011-0","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0022-247x(74)90011-0","pdf_url":"https://www.sciencedirect.com/science/article/pii/0022247X74900110/pdf","source":{"id":"https://openalex.org/S151579836","display_name":"Journal of Mathematical Analysis and Applications","issn_l":"0022-247X","issn":["0022-247X","1096-0813"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Analysis and Applications","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/W1995253776.pdf","grobid_xml":"https://content.openalex.org/works/W1995253776.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2007440904","https://openalex.org/W2026261958","https://openalex.org/W2030133680","https://openalex.org/W2081079571"],"related_works":["https://openalex.org/W252725567","https://openalex.org/W321451563","https://openalex.org/W1981578676","https://openalex.org/W7020647186","https://openalex.org/W7142299164","https://openalex.org/W2011847242","https://openalex.org/W204573694","https://openalex.org/W1998235755","https://openalex.org/W7100707277","https://openalex.org/W2324136073"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}