{"id":"https://openalex.org/W1963647670","doi":"https://doi.org/10.1134/s000143460809023x","title":"On the uniqueness criterion for solutions of the Sturm-Liouville equation","display_name":"On the uniqueness criterion for solutions of the Sturm-Liouville equation","publication_year":2008,"publication_date":"2008-10-01","ids":{"openalex":"https://openalex.org/W1963647670","doi":"https://doi.org/10.1134/s000143460809023x","mag":"1963647670"},"language":"en","primary_location":{"id":"doi:10.1134/s000143460809023x","doi":"https://doi.org/10.1134/s000143460809023x","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s000143460809023x","pdf_url":null,"source":{"id":"https://openalex.org/S16116274","display_name":"Mathematical Notes","issn_l":"0001-4346","issn":["0001-4346","1067-9073","1573-8876"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-2"],"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":"Mathematical Notes","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/A5028451661","display_name":"Kh. K. Ishkin","orcid":"https://orcid.org/0000-0002-4943-9079","observed_orcids":["https://orcid.org/0000-0002-4943-9079"]},"institutions":[{"id":"https://openalex.org/I138958963","display_name":"Bashkir State University","ror":"https://ror.org/04gr31p94","country_code":"RU","type":"education","lineage":["https://openalex.org/I138958963","https://openalex.org/I4387155162"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Kh. K. Ishkin","raw_affiliation_strings":["Bashkiria State University, Ufa, Russia","Bashkiria State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bashkiria State University, Ufa, Russia","institution_ids":["https://openalex.org/I138958963"]},{"raw_affiliation_string":"Bashkiria State University","institution_ids":["https://openalex.org/I138958963"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028451661"],"corresponding_institution_ids":["https://openalex.org/I138958963"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.06754818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":95},"biblio":{"volume":"84","issue":"3-4","first_page":"515","last_page":"528"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9887999892234802,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9887999892234802,"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"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.0032999999821186066,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.0031999999191612005,"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/sturm-liouville-equation","display_name":"Sturm-Liouville equation","score":0.9629999995231628},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.8870000243186951},{"id":"https://openalex.org/keywords/annular-domains","display_name":"annular domains","score":0.6150000095367432},{"id":"https://openalex.org/keywords/complex-plane","display_name":"complex plane","score":0.49799999594688416},{"id":"https://openalex.org/keywords/necessary-and-sufficient-conditions","display_name":"necessary and sufficient conditions","score":0.7419999837875366},{"id":"https://openalex.org/keywords/eigenvalue-parameter","display_name":"eigenvalue parameter","score":0.5580000281333923},{"id":"https://openalex.org/keywords/second-order-differential-equations","display_name":"second-order differential equations","score":0.5569999814033508}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9024624228477478},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8051764965057373},{"id":"https://openalex.org/C22892174","wikidata":"https://www.wikidata.org/wiki/Q1154082","display_name":"Sturm\u2013Liouville theory","level":3,"score":0.7731695175170898},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.7244719862937927},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6784644722938538},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5789217948913574},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33506736159324646},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.10016188025474548},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0728808045387268},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s000143460809023x","doi":"https://doi.org/10.1134/s000143460809023x","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s000143460809023x","pdf_url":null,"source":{"id":"https://openalex.org/S16116274","display_name":"Mathematical Notes","issn_l":"0001-4346","issn":["0001-4346","1067-9073","1573-8876"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["anvur-scientific","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-2"],"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":"Mathematical Notes","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":17,"referenced_works":["https://openalex.org/W606671493","https://openalex.org/W1575147392","https://openalex.org/W1592958377","https://openalex.org/W1803017756","https://openalex.org/W2016019465","https://openalex.org/W2040577723","https://openalex.org/W2064958022","https://openalex.org/W2327910720","https://openalex.org/W2329776404","https://openalex.org/W2597468651","https://openalex.org/W2742470390","https://openalex.org/W2990934340","https://openalex.org/W3038830718","https://openalex.org/W3046782287","https://openalex.org/W3141151088","https://openalex.org/W4285719527","https://openalex.org/W4299150230"],"related_works":["https://openalex.org/W61872118","https://openalex.org/W4298160827","https://openalex.org/W2765780482","https://openalex.org/W2361572927","https://openalex.org/W2037895326","https://openalex.org/W2029357119","https://openalex.org/W2024932957","https://openalex.org/W1984370280","https://openalex.org/W2072572531","https://openalex.org/W2153356214"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,29,37,58,65],"Sturm-Liouville":[3],"equation":[4,38],"$$":[5,14],"-":[6],"y''":[7],"+":[8,40],"qy":[9],"=":[10,42],"\\lambda":[11],"^2":[12],"y":[13],"in":[15,57],"an":[16],"annular":[17],"domain":[18,59],"K":[19,60],"from":[20],"\u2102":[21],"and":[22,25],"obtain":[23],"necessary":[24],"sufficient":[26],"conditions":[27],"on":[28],"potential":[30],"q":[31],"under":[32],"which":[33],"all":[34,62],"solutions":[35],"of":[36,64],"\u2212y\u2033(z)":[39],"q(z)y(z)":[41],"\u03bb":[43,67],"2":[44],"y(z),":[45],"z":[46],"\u2208":[47,68],"\u03b3,":[48],"where":[49],"\u03b3":[50],"is":[51],"a":[52],"certain":[53],"curve,":[54],"are":[55],"unique":[56],"for":[61],"values":[63],"parameter":[66],"\u2102.":[69]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-09-21T07:43:02.447757","created_date":"2016-06-24T00:00:00"}
