{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T17:55:37Z","timestamp":1772819737310,"version":"3.50.1"},"reference-count":43,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["DCDS-S"],"published-print":{"date-parts":[[2018]]},"DOI":"10.3934\/dcdss.2018057","type":"journal-article","created":{"date-parts":[[2018,6,4]],"date-time":"2018-06-04T23:34:10Z","timestamp":1528155250000},"page":"963-990","source":"Crossref","is-referenced-by-count":4,"title":["One-dimensional, non-local, first-order stationary mean-field games with congestion: A Fourier approach"],"prefix":"10.3934","volume":"11","author":[{"given":"Levon","family":"Nurbekyan","sequence":"first","affiliation":[]}],"member":"2321","reference":[{"key":"key-10.3934\/dcdss.2018057-1","doi-asserted-by":"publisher","unstructured":"Y. Achdou, Finite difference methods for mean field games, in <i>Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications<\/i>, vol. 2074 of Lecture Notes in Math., Springer, Heidelberg, 2013, 1\u201347.","DOI":"10.1007\/978-3-642-36433-4_1"},{"key":"key-10.3934\/dcdss.2018057-2","doi-asserted-by":"publisher","DOI":"10.1137\/100790069"},{"key":"key-10.3934\/dcdss.2018057-3","doi-asserted-by":"publisher","DOI":"10.1137\/090758477"},{"key":"key-10.3934\/dcdss.2018057-4","doi-asserted-by":"publisher","DOI":"10.3934\/nhm.2012.7.197"},{"key":"key-10.3934\/dcdss.2018057-5","doi-asserted-by":"publisher","DOI":"10.1137\/15M1015455"},{"key":"key-10.3934\/dcdss.2018057-6","doi-asserted-by":"publisher","DOI":"10.1007\/s13235-016-0203-5"},{"key":"key-10.3934\/dcdss.2018057-7","doi-asserted-by":"publisher","DOI":"10.3934\/nhm.2012.7.263"},{"key":"key-10.3934\/dcdss.2018057-8","unstructured":"P. Cardaliaguet, <i>Notes on Mean Field Games<\/i>, 2013, URL <a href=\"https:\/\/www.ceremade.dauphine.fr\/~cardaliaguet\/MFG20130420.pdf\" target=\"_blank\">https:\/\/www.ceremade.dauphine.fr\/~cardaliaguet\/MFG20130420.pdf<\/a>."},{"key":"key-10.3934\/dcdss.2018057-9","doi-asserted-by":"publisher","unstructured":"P. Cardaliaguet, Weak solutions for first order mean field games with local coupling, in <i>Analysis and Geometry in Control Theory and Its Applications<\/i>, vol. 11 of Springer INdAM Ser., Springer, Cham, 2015, 111\u2013158.","DOI":"10.1007\/978-3-319-06917-3_5"},{"key":"key-10.3934\/dcdss.2018057-10","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-015-0323-4"},{"key":"key-10.3934\/dcdss.2018057-11","doi-asserted-by":"publisher","DOI":"10.1137\/15M1029849"},{"key":"key-10.3934\/dcdss.2018057-12","doi-asserted-by":"publisher","DOI":"10.1137\/120902987"},{"key":"key-10.3934\/dcdss.2018057-13","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2016.1192647"},{"key":"key-10.3934\/dcdss.2018057-14","doi-asserted-by":"crossref","unstructured":"J. Duoandikoetxea, <i>Fourier Analysis<\/i>, vol. 29 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2001, Translated and revised from the 1995 Spanish original by David Cruz-Uribe","DOI":"10.1090\/gsm\/029"},{"key":"key-10.3934\/dcdss.2018057-15","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-017-9615-1"},{"key":"key-10.3934\/dcdss.2018057-16","unstructured":"R. Ferreira and D. Gomes, Existence of weak solutions for stationary mean-field games through variational inequalities, arXiv preprint, arXiv: 1512.05828, [math. AP]."},{"key":"key-10.3934\/dcdss.2018057-17","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-015-0349-7"},{"key":"key-10.3934\/dcdss.2018057-18","doi-asserted-by":"publisher","unstructured":"D. Gomes, L. Nurbekyan and M. Prazeres, Explicit solutions of one-dimensional, first-order, stationary mean-field games with congestion, in <i>2016 IEEE 55th Conference on Decision and Control (CDC)<\/i>, 2016, 4534\u20134539.","DOI":"10.1109\/CDC.2016.7798959"},{"key":"key-10.3934\/dcdss.2018057-19","doi-asserted-by":"publisher","DOI":"10.1007\/s13235-017-0223-9"},{"key":"key-10.3934\/dcdss.2018057-20","doi-asserted-by":"publisher","DOI":"10.1137\/140984622"},{"key":"key-10.3934\/dcdss.2018057-21"},{"key":"key-10.3934\/dcdss.2018057-22","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2014.903574"},{"key":"key-10.3934\/dcdss.2018057-23","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2015029"},{"key":"key-10.3934\/dcdss.2018057-24","doi-asserted-by":"publisher","unstructured":"D. Gomes, E. Pimentel and V. Voskanyan, <i>Regularity Theory for Mean-Field Game Systems<\/i>, SpringerBriefs in Mathematics, Springer, [Cham], 2016.","DOI":"10.1007\/978-3-319-38934-9"},{"key":"key-10.3934\/dcdss.2018057-25","doi-asserted-by":"publisher","DOI":"10.3934\/nhm.2012.7.303"},{"key":"key-10.3934\/dcdss.2018057-26","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2013-05936-3"},{"key":"key-10.3934\/dcdss.2018057-27","doi-asserted-by":"publisher","DOI":"10.1007\/s13235-013-0099-2"},{"key":"key-10.3934\/dcdss.2018057-28","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/jdv052"},{"key":"key-10.3934\/dcdss.2018057-29","unstructured":"J. Graber, Weak solutions for mean field games with congestion, arXiv preprint, URL <a href=\"https:\/\/arXiv.org\/abs\/1503.04733\" target=\"_blank\">https:\/\/arXiv.org\/abs\/1503.04733<\/a>, arXiv: 1503.04733v3 [math. AP]."},{"key":"key-10.3934\/dcdss.2018057-30","doi-asserted-by":"publisher","DOI":"10.3934\/nhm.2012.7.315"},{"key":"key-10.3934\/dcdss.2018057-31","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-014-9280-2"},{"key":"key-10.3934\/dcdss.2018057-32","doi-asserted-by":"publisher","unstructured":"O. Gu\u00e9ant, J. -M. Lasry and P. -L. Lions, Mean field games and applications, in <i>ParisPrinceton Lectures on Mathematical Finance 2010<\/i>, vol. 2003 of Lecture Notes in Math., Springer, Berlin, 2011, 205\u2013266","DOI":"10.1007\/978-3-642-14660-2_3"},{"key":"key-10.3934\/dcdss.2018057-33","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2007.904450"},{"key":"key-10.3934\/dcdss.2018057-34","doi-asserted-by":"publisher","DOI":"10.4310\/CIS.2006.v6.n3.a5"},{"key":"key-10.3934\/dcdss.2018057-35","doi-asserted-by":"publisher","unstructured":"J. -M. Lasry and P. -L. Lions, Mean field games, <i>Japanese Journal of Mathematics<\/i>, <b>2<\/b> (2007), 229\u2013260, URL <a href=\"http:\/\/www.ifd.dauphine.fr\/fileadmin\/mediatheque\/recherche_et_valo\/FDD\/Cahier_Chaire_2.pdf\" target=\"_blank\">http:\/\/www.ifd.dauphine.fr\/fileadmin\/mediatheque\/recherche_et_valo\/FDD\/Cahier_Chaire_2.pdf<\/a>.","DOI":"10.1007\/s11537-007-0657-8"},{"key":"key-10.3934\/dcdss.2018057-36","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2006.09.019"},{"key":"key-10.3934\/dcdss.2018057-37","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2006.09.018"},{"key":"key-10.3934\/dcdss.2018057-38","doi-asserted-by":"publisher","DOI":"10.1007\/s11537-007-0657-8"},{"key":"key-10.3934\/dcdss.2018057-39","unstructured":"P. -L. Lions, College de France course on mean-field games, URL <a href=\"https:\/\/www.college-de-france.fr\/site\/en-pierre-louis-lions\/_course.htm\" target=\"_blank\">https:\/\/www.college-de-france.fr\/site\/en-pierre-louis-lions\/_course.htm<\/a>."},{"key":"key-10.3934\/dcdss.2018057-40","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2015.07.008"},{"key":"key-10.3934\/dcdss.2018057-41","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2017.66.5944"},{"key":"key-10.3934\/dcdss.2018057-42","doi-asserted-by":"publisher","DOI":"10.1007\/s13235-013-0080-0"},{"key":"key-10.3934\/dcdss.2018057-43","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-014-0799-9"}],"container-title":["Discrete and Continuous Dynamical Systems - S"],"original-title":[],"link":[{"URL":"https:\/\/aimsciences.org\/download\/files\/1937-1632_2018_5_963.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T11:46:31Z","timestamp":1772797591000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.aimsciences.org\/\/article\/doi\/10.3934\/dcdss.2018057"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"references-count":43,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2018]]}},"URL":"https:\/\/doi.org\/10.3934\/dcdss.2018057","relation":{},"ISSN":["1937-1632","1937-1179"],"issn-type":[{"value":"1937-1632","type":"print"},{"value":"1937-1179","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018]]}}}