{"id":"https://openalex.org/W2221072259","doi":"https://doi.org/10.1007/978-1-4615-9828-2_17","title":"Generalized Solutions to Ordinary Differential Equations with Discontinuous Right-Hand Sides Via \u0393-Convergence","display_name":"Generalized Solutions to Ordinary Differential Equations with Discontinuous Right-Hand Sides Via \u0393-Convergence","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W2221072259","doi":"https://doi.org/10.1007/978-1-4615-9828-2_17","mag":"2221072259"},"language":"en","primary_location":{"id":"doi:10.1007/978-1-4615-9828-2_17","doi":"https://doi.org/10.1007/978-1-4615-9828-2_17","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4615-9828-2_17","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Partial Differential Equations and the Calculus of Variations","raw_type":"book-chapter"},"volume":{"id":"https://openalex.org/W2476097747","display_name":"Partial Differential Equations and the Calculus of Variations"},"type":"book-chapter","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/A5044610577","display_name":"Zofia Denkowska","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Zofia Denkowska","raw_affiliation_strings":["Institute for Information Sciences, Jagellonian University, Krakow, Poland","Institute of Mathematics, Jagellonian University, Krakow, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Information Sciences, Jagellonian University, Krakow, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"Institute of Mathematics, Jagellonian University, Krakow, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025064025","display_name":"Zdzis\u0142aw Denkowski","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Zdzislaw Denkowski","raw_affiliation_strings":["Institute for Information Sciences, Jagellonian University, Krakow, Poland","Institute of Mathematics, Jagellonian University, Krakow, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Information Sciences, Jagellonian University, Krakow, Poland","institution_ids":["https://openalex.org/I126596746"]},{"raw_affiliation_string":"Institute of Mathematics, Jagellonian University, Krakow, Poland","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I126596746"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.27799607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"371","last_page":"400"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9897000193595886,"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":0.9897000193595886,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.0017999999690800905,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.00139999995008111,"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/ordinary-differential-equations","display_name":"ordinary differential equations","score":0.796999990940094},{"id":"https://openalex.org/keywords/discontinuous-right-hand-side","display_name":"discontinuous right-hand side","score":0.9129999876022339},{"id":"https://openalex.org/keywords/gamma-convergence","display_name":"Gamma-convergence","score":0.8930000066757202},{"id":"https://openalex.org/keywords/weak-solutions","display_name":"weak solutions","score":0.8429999947547913},{"id":"https://openalex.org/keywords/delayed-arguments","display_name":"retarded argument","score":0.41499999165534973},{"id":"https://openalex.org/keywords/borel-functions","display_name":"Borel functions","score":0.7590000033378601},{"id":"https://openalex.org/keywords/filippov-solutions","display_name":"Filippov solutions","score":0.8109999895095825},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.6359999775886536},{"id":"https://openalex.org/keywords/projection-theorem","display_name":"projection theorem","score":0.593999981880188},{"id":"https://openalex.org/keywords/minimization-of-functionals","display_name":"functional minimization","score":0.5709999799728394}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8704071044921875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8375339508056641},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.619132399559021},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5925968289375305},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5394870042800903},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47371333837509155},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43421387672424316},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.4275369942188263},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4248933792114258},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3900916278362274},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38219955563545227},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.26317107677459717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07376056909561157},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-1-4615-9828-2_17","doi":"https://doi.org/10.1007/978-1-4615-9828-2_17","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-1-4615-9828-2_17","pdf_url":null,"source":{"id":"https://openalex.org/S4306462921","display_name":"Birkh\u00e4user Boston eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Partial Differential Equations and the Calculus of Variations","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W34632080","https://openalex.org/W47254212","https://openalex.org/W768370832","https://openalex.org/W1527244075","https://openalex.org/W1531856058","https://openalex.org/W1592648094","https://openalex.org/W1997463214","https://openalex.org/W2005362598","https://openalex.org/W2013247359","https://openalex.org/W2044978307","https://openalex.org/W2094871536","https://openalex.org/W2118986540","https://openalex.org/W2480138449","https://openalex.org/W4210718478","https://openalex.org/W4246266336","https://openalex.org/W6607880535"],"related_works":["https://openalex.org/W129680301","https://openalex.org/W3047897649","https://openalex.org/W7096796105","https://openalex.org/W1992104072","https://openalex.org/W7096749088","https://openalex.org/W2492898584","https://openalex.org/W2393550196","https://openalex.org/W7028459783","https://openalex.org/W1485526214","https://openalex.org/W634144898"],"abstract_inverted_index":{"In":[0,44,117],"the":[1,50,76,111,121,129,133],"present":[2],"paper":[3,122],"we":[4,47,79],"develop":[5],"an":[6,123],"idea":[7],"of":[8,26,32,36,98,105,113,120],"Prof.E.":[9],"De":[10,100],"Giorgi,":[11],"which":[12],"can":[13],"be":[14,22],"formulated":[15],"as":[16,24,75],"follows:":[17],"\u201csolutions":[18],"to":[19,59,69],"ODE":[20,60,70],"may":[21],"obtained":[23],"minimizers":[25],"some":[27],"functionals":[28,37,57,67],"that":[29],"are":[30,108],"\u0393-limits":[31],"appropriately":[33],"chosen":[34],"sequences":[35],"defined":[38],"on":[39],"suitable":[40],"functional":[41],"spaces":[42],"\u201d.":[43],"this":[45,118],"way":[46],"obtain":[48],"immediately":[49],"existence":[51],"ot":[52],"Uaratheodory":[53],"solutions":[54,82,107,115],"(C-solutions)":[55],"using":[56,65],"conneted":[58],"with":[61,141],"retarded":[62],"argument.":[63],"Next,":[64],"other":[66],"connected":[68],"having":[71],"a":[72],"Borel":[73],"function":[74],"right-hand":[77],"side,":[78],"get":[80],"generalized":[81,106],"\u2014":[83],"so":[84],"called":[85],"K-solutions":[86],"(Krasowskii":[87],"solutions)":[88],"and":[89,132],"D-solutions":[90,95],"(we":[91],"have":[92],"named":[93],"them":[94],"in":[96],"honour":[97],"Prof.":[99],"Giorgi).":[101],"Both":[102],"these":[103],"classes":[104],"different":[109],"from":[110],"class":[112],"Filippov":[114],"(F-solutions).":[116],"part":[119],"important":[124],"role":[125],"is":[126],"played":[127],"by":[128],"projection":[130],"theorem":[131,136],"Au-mann":[134],"selection":[135],"for":[137],"measurable":[138],"multivalued":[139],"functions":[140],"not":[142],"necessarily":[143],"closed":[144],"values.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2016-06-24T00:00:00"}