{"id":"https://openalex.org/W2018183341","doi":"https://doi.org/10.1134/s0012266107070178","title":"A priori estimate and existence of periodic solutions for a certain class of systems of nonlinear second-order ordinary differential equations on the plane","display_name":"A priori estimate and existence of periodic solutions for a certain class of systems of nonlinear second-order ordinary differential equations on the plane","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2018183341","doi":"https://doi.org/10.1134/s0012266107070178","mag":"2018183341"},"language":"en","primary_location":{"id":"doi:10.1134/s0012266107070178","doi":"https://doi.org/10.1134/s0012266107070178","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0012266107070178","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/A5073508813","display_name":"\u0410. \u041d. \u041d\u0430\u0438\u043c\u043e\u0432","orcid":"https://orcid.org/0000-0002-6194-7164","observed_orcids":["https://orcid.org/0000-0002-6194-7164"]},"institutions":[{"id":"https://openalex.org/I137513774","display_name":"Vologda State University","ror":"https://ror.org/05hcp8p49","country_code":"RU","type":"education","lineage":["https://openalex.org/I137513774"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A. N. Naimov","raw_affiliation_strings":["Vologda State Technical University, Vologda, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Vologda State Technical University, Vologda, Russia","institution_ids":["https://openalex.org/I137513774"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073508813"],"corresponding_institution_ids":["https://openalex.org/I137513774"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"43","issue":"7","first_page":"1025","last_page":"1030"},"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":0.861299991607666,"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":0.861299991607666,"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":0.13369999825954437,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/a-priori-estimates","display_name":"a priori estimates","score":0.9210000038146973},{"id":"https://openalex.org/keywords/existence-of-periodic-solutions","display_name":"existence of periodic solutions","score":0.921999990940094},{"id":"https://openalex.org/keywords/second-order-nonlinear-differential-equations","display_name":"second-order nonlinear differential equations","score":0.9210000038146973},{"id":"https://openalex.org/keywords/systems-of-differential-equations","display_name":"systems of differential equations","score":0.7889999747276306},{"id":"https://openalex.org/keywords/planar-differential-equations","display_name":"planar differential equations","score":0.7020000219345093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8622868061065674},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.794967532157898},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6506836414337158},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6265122890472412},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6216577291488647},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.579833984375},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.48904237151145935},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46099853515625},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.43032291531562805},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41448405385017395},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.39818429946899414},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0904933512210846},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05611047148704529},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0012266107070178","doi":"https://doi.org/10.1134/s0012266107070178","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s0012266107070178","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W3145075304","https://openalex.org/W6606801652"],"related_works":["https://openalex.org/W4285274545","https://openalex.org/W2046377615","https://openalex.org/W4412486664","https://openalex.org/W2036956178","https://openalex.org/W4414703275","https://openalex.org/W4405240777","https://openalex.org/W4402171450","https://openalex.org/W1999025916","https://openalex.org/W7171306571","https://openalex.org/W1980743457"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}