{"id":"https://openalex.org/W2023779261","doi":"https://doi.org/10.1016/0022-247x(76)90024-x","title":"Sturm transformations and linear hyperbolic differential equations in two variables","display_name":"Sturm transformations and linear hyperbolic differential equations in two variables","publication_year":1976,"publication_date":"1976-12-01","ids":{"openalex":"https://openalex.org/W2023779261","doi":"https://doi.org/10.1016/0022-247x(76)90024-x","mag":"2023779261"},"language":"en","primary_location":{"id":"doi:10.1016/0022-247x(76)90024-x","doi":"https://doi.org/10.1016/0022-247x(76)90024-x","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0022-247x(76)90024-x","pdf_url":null,"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://doi.org/10.1016/0022-247x(76)90024-x","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074940124","display_name":"Donald R. Smith","orcid":"https://orcid.org/0000-0002-4919-1042","observed_orcids":["https://orcid.org/0000-0002-4919-1042"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Donald R Smith","raw_affiliation_strings":["Department of Mathematics, University of California at San Diego, P.O. Box 109, La Jolla, California 92037 U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California at San Diego, P.O. Box 109, La Jolla, California 92037 U.S.A","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000293104","display_name":"Mills B. Weinstein","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mills B Weinstein","raw_affiliation_strings":["University of California at San Diego, P.O. Box 109, La Jolla, California 92037 U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California at San Diego, P.O. Box 109, La Jolla, California 92037 U.S.A","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":0.6403,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6573475,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":96},"biblio":{"volume":"56","issue":"3","first_page":"548","last_page":"566"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.8353999853134155,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.8353999853134155,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.019099999219179153,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.016100000590085983,"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/linear-hyperbolic-equations","display_name":"linear hyperbolic equations","score":0.8600000143051147},{"id":"https://openalex.org/keywords/second-order-partial-differential-equations","display_name":"second-order partial differential equations","score":0.7379999756813049},{"id":"https://openalex.org/keywords/two-independent-variables","display_name":"two independent variables","score":0.6840000152587891},{"id":"https://openalex.org/keywords/canonical-form","display_name":"canonical form","score":0.39399999380111694},{"id":"https://openalex.org/keywords/variable-transformation","display_name":"change of variables","score":0.36500000953674316}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8971518278121948},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.7002628445625305},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5041881799697876},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.46132200956344604},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.4564395844936371},{"id":"https://openalex.org/C92047909","wikidata":"https://www.wikidata.org/wiki/Q204034","display_name":"Hyperbolic function","level":2,"score":0.4205017685890198},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35920852422714233},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33353865146636963}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0022-247x(76)90024-x","doi":"https://doi.org/10.1016/0022-247x(76)90024-x","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0022-247x(76)90024-x","pdf_url":null,"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(76)90024-x","doi":"https://doi.org/10.1016/0022-247x(76)90024-x","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0022-247x(76)90024-x","pdf_url":null,"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1645588759","https://openalex.org/W1982574474","https://openalex.org/W1994943121","https://openalex.org/W2019342669","https://openalex.org/W2021298391","https://openalex.org/W2029438103","https://openalex.org/W2040187963","https://openalex.org/W2041403360","https://openalex.org/W2046904024","https://openalex.org/W2120514963","https://openalex.org/W2323871049","https://openalex.org/W2324033510","https://openalex.org/W2504713890","https://openalex.org/W2590975118","https://openalex.org/W3002379364","https://openalex.org/W4248784639","https://openalex.org/W6823835578"],"related_works":["https://openalex.org/W2015118256","https://openalex.org/W2038431206","https://openalex.org/W2092912693","https://openalex.org/W2734410470","https://openalex.org/W7223519594","https://openalex.org/W594321253","https://openalex.org/W2018256431","https://openalex.org/W4231168057","https://openalex.org/W1988639536","https://openalex.org/W2363927089"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2016-06-24T00:00:00"}
