{"id":"https://openalex.org/W2056018340","doi":"https://doi.org/10.1007/s00182-006-0030-9","title":"Zero-sum state constrained differential games: existence of value for Bolza problem","display_name":"Zero-sum state constrained differential games: existence of value for Bolza problem","publication_year":2006,"publication_date":"2006-09-09","ids":{"openalex":"https://openalex.org/W2056018340","doi":"https://doi.org/10.1007/s00182-006-0030-9","mag":"2056018340"},"language":"en","primary_location":{"id":"doi:10.1007/s00182-006-0030-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00182-006-0030-9","pdf_url":null,"source":{"id":"https://openalex.org/S132210109","display_name":"International Journal of Game Theory","issn_l":"0020-7276","issn":["0020-7276","1432-1270"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Game Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://basepub.dauphine.psl.eu/handle/123456789/26085","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109351634","display_name":"Piernicola Bettiol","orcid":"https://orcid.org/0000-0003-4969-6144"},"institutions":[{"id":"https://openalex.org/I2802204017","display_name":"Universit\u00e9 de Bretagne Sud","ror":"https://ror.org/04ed7fw48","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802204017"]},{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]},{"id":"https://openalex.org/I4210119023","display_name":"Laboratoire de Math\u00e9matiques de Bretagne Atlantique","ror":"https://ror.org/02ght4n58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802204017","https://openalex.org/I4210119023","https://openalex.org/I4210141950","https://openalex.org/I4412460332"]}],"countries":["FR","IT"],"is_corresponding":true,"raw_author_name":"Piernicola Bettiol","raw_affiliation_strings":["SISSA/ISAS, via Beirut 2-4, 34013, Trieste, Italy","UBO - Universit\u00e9 de Brest (Universit\u00e9 de Bretagne Occidentale - 3 Rue des Archives 29238, Brest - France)","LMBA - Laboratoire de Math\u00e9matiques de Bretagne Atlantique (Universit\u00e9 de Brest, 6 avenue Le Gorgeu, CS 93837, 29238 Brest cedex 3 / Universit\u00e9 de Bretagne-Sud, Centre Yves Coppens, B\u00e2t. B, Campus de Tohannic, BP 573, 56017 Vannes - France)"],"affiliations":[{"raw_affiliation_string":"SISSA/ISAS, via Beirut 2-4, 34013, Trieste, Italy","institution_ids":["https://openalex.org/I138549579"]},{"raw_affiliation_string":"UBO - Universit\u00e9 de Brest (Universit\u00e9 de Bretagne Occidentale - 3 Rue des Archives 29238, Brest - France)","institution_ids":["https://openalex.org/I161929037"]},{"raw_affiliation_string":"LMBA - Laboratoire de Math\u00e9matiques de Bretagne Atlantique (Universit\u00e9 de Brest, 6 avenue Le Gorgeu, CS 93837, 29238 Brest cedex 3 / Universit\u00e9 de Bretagne-Sud, Centre Yves Coppens, B\u00e2t. B, Campus de Tohannic, BP 573, 56017 Vannes - France)","institution_ids":["https://openalex.org/I2802204017","https://openalex.org/I161929037","https://openalex.org/I4210119023"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032926943","display_name":"Pierre Cardaliaguet","orcid":"https://orcid.org/0000-0002-9322-6783"},"institutions":[{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]},{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Cardaliaguet","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, 29200, Brest, France","CEREMADE - CEntre de REcherches en MAth\u00e9matiques de la DEcision (Place du Mar\u00e9chal de Lattre de Tassigny 75775 - Paris Cedex 16 - France)"],"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, 29200, Brest, France","institution_ids":["https://openalex.org/I161929037","https://openalex.org/I3019441195"]},{"raw_affiliation_string":"CEREMADE - CEntre de REcherches en MAth\u00e9matiques de la DEcision (Place du Mar\u00e9chal de Lattre de Tassigny 75775 - Paris Cedex 16 - France)","institution_ids":["https://openalex.org/I171048554"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044513568","display_name":"Marc Quincampoix","orcid":"https://orcid.org/0009-0004-4223-2720"},"institutions":[{"id":"https://openalex.org/I3019441195","display_name":"Laboratoire de Math\u00e9matiques d'Orsay","ror":"https://ror.org/03ab0zs98","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I3019441195"]},{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I4210119023","display_name":"Laboratoire de Math\u00e9matiques de Bretagne Atlantique","ror":"https://ror.org/02ght4n58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802204017","https://openalex.org/I4210119023","https://openalex.org/I4210141950","https://openalex.org/I4412460332"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Marc Quincampoix","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, 29200, Brest, France","LM - Laboratoire de math\u00e9matiques de Brest (6 avenue Victor le Gorgeu - BP 93837 29285 BREST CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Bretagne Occidentale, 6 Avenue Victor Le Gorgeu, 29200, Brest, France","institution_ids":["https://openalex.org/I161929037","https://openalex.org/I3019441195"]},{"raw_affiliation_string":"LM - Laboratoire de math\u00e9matiques de Brest (6 avenue Victor le Gorgeu - BP 93837 29285 BREST CEDEX - France)","institution_ids":["https://openalex.org/I4210119023"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109351634"],"corresponding_institution_ids":["https://openalex.org/I138549579","https://openalex.org/I161929037","https://openalex.org/I2802204017","https://openalex.org/I4210119023"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.5853,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.94013587,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"34","issue":"4","first_page":"495","last_page":"527"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9965999722480774,"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"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9965999722480774,"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"}},{"id":"https://openalex.org/T14083","display_name":"Extremum Seeking Control Systems","score":0.9879999756813049,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9818999767303467,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8339178562164307},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6770514845848083},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.6626626253128052},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.59424889087677},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5853316783905029},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5574048757553101},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.533894419670105},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.5219994783401489},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5003378391265869},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.46065422892570496},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45032799243927},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.43796199560165405},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.4289754033088684},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37874335050582886},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3720528185367584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36111435294151306},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.24409440159797668},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20316988229751587},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08241662383079529},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06692168116569519}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8339178562164307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6770514845848083},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.6626626253128052},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.59424889087677},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5853316783905029},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5574048757553101},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.533894419670105},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.5219994783401489},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5003378391265869},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.46065422892570496},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45032799243927},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.43796199560165405},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.4289754033088684},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37874335050582886},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3720528185367584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36111435294151306},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.24409440159797668},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20316988229751587},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08241662383079529},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06692168116569519},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/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},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00182-006-0030-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00182-006-0030-9","pdf_url":null,"source":{"id":"https://openalex.org/S132210109","display_name":"International Journal of Game Theory","issn_l":"0020-7276","issn":["0020-7276","1432-1270"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Game Theory","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04404455v1","is_oa":false,"landing_page_url":"https://hal.univ-brest.fr/hal-04404455","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://link.springer.com/article/10.1007/s00182-006-0030-9","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:spr:jogath:v:34:y:2006:i:4:p:495-527","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s00182-006-0030-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:basepub.dauphine.psl.eu:123456789/26085","is_oa":true,"landing_page_url":"https://basepub.dauphine.psl.eu/handle/123456789/26085","pdf_url":null,"source":{"id":"https://openalex.org/S4306401007","display_name":"Base Institutionnelle de Recherche de l'universit\u00e9 Paris-Dauphine (BIRD) (University Paris-Dauphine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102197404","host_organization_name":"Universit\u00e9 Paris-Sud","host_organization_lineage":["https://openalex.org/I102197404"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article accept\u00e9 pour publication ou publi\u00e9"}],"best_oa_location":{"id":"pmh:oai:basepub.dauphine.psl.eu:123456789/26085","is_oa":true,"landing_page_url":"https://basepub.dauphine.psl.eu/handle/123456789/26085","pdf_url":null,"source":{"id":"https://openalex.org/S4306401007","display_name":"Base Institutionnelle de Recherche de l'universit\u00e9 Paris-Dauphine (BIRD) (University Paris-Dauphine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102197404","host_organization_name":"Universit\u00e9 Paris-Sud","host_organization_lineage":["https://openalex.org/I102197404"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article accept\u00e9 pour publication ou publi\u00e9"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W635295581","https://openalex.org/W1487586009","https://openalex.org/W1505284970","https://openalex.org/W1547240457","https://openalex.org/W1550828720","https://openalex.org/W1607363710","https://openalex.org/W1879112630","https://openalex.org/W1994996557","https://openalex.org/W1999987512","https://openalex.org/W2000958946","https://openalex.org/W2017696099","https://openalex.org/W2056616297","https://openalex.org/W2071653719","https://openalex.org/W2072575566","https://openalex.org/W2074983280","https://openalex.org/W2082133068","https://openalex.org/W2083331171","https://openalex.org/W2088907413","https://openalex.org/W2141616022","https://openalex.org/W2462614204","https://openalex.org/W2612952478","https://openalex.org/W2749408143","https://openalex.org/W2888914392","https://openalex.org/W4251849361"],"related_works":["https://openalex.org/W4287078947","https://openalex.org/W4297940580","https://openalex.org/W1654696814","https://openalex.org/W2954291171","https://openalex.org/W2088353628","https://openalex.org/W2313187187","https://openalex.org/W2032834442","https://openalex.org/W2117494769","https://openalex.org/W2950973671","https://openalex.org/W3124904228"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}