{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:20:48Z","timestamp":1773656448739,"version":"3.50.1"},"reference-count":29,"publisher":"Pleiades Publishing Ltd","issue":"11","license":[{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Autom Remote Control"],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1134\/s0005117921110151","type":"journal-article","created":{"date-parts":[[2021,12,22]],"date-time":"2021-12-22T10:15:27Z","timestamp":1640168127000},"page":"2006-2023","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Differential Games in a Banach Space on a Fixed Chain"],"prefix":"10.1134","volume":"82","author":[{"given":"A. V.","family":"Chernov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"137","published-online":{"date-parts":[[2021,12,22]]},"reference":[{"key":"2211_CR1","volume-title":"Fizika poluprovodnikov (Semiconductor Physics)","author":"V.L. Bonch-Bruevich","year":"1990","unstructured":"Bonch-Bruevich, V.L. and Kalashnikov, S.G., Fizika\npoluprovodnikov (Semiconductor Physics), Moscow:\nNauka, 1990."},{"issue":"11","key":"2211_CR2","first-page":"1861","volume":"31","author":"F.P. Vasil\u2019ev","year":"1995","unstructured":"Vasil\u2019ev, F.P., Duality in linear control and observation problems, Differ. Equations, 1995, vol. 31, no. 11,\npp. 1861\u20131868.","journal-title":"Differ. Equations"},{"issue":"4","key":"2211_CR3","first-page":"71","volume":"20","author":"A.A. Vlasenko","year":"2014","unstructured":"Vlasenko, A.A. and Chikrii, A.A., On a differential game in a distributed\nparameter system, Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad.\nNauk, 2014, vol. 20, no. 4, pp. 71\u201380.","journal-title":"Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk"},{"issue":"2","key":"2211_CR4","first-page":"26","volume":"21","author":"A.A. Vlasenko","year":"2015","unstructured":"Vlasenko, A.A., Rutkas, A.G., and Chikrii, A.A., On a differential game in an\nabstract parabolic system, Tr. Inst. Mat. Mekh. Ural. Otd. Ross.\nAkad. Nauk, 2015, vol. 21, no. 2, pp. 26\u201340.","journal-title":"Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk"},{"key":"2211_CR5","doi-asserted-by":"crossref","DOI":"10.1515\/9783112717899","volume-title":"Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen","author":"H. Gajewski","year":"1974","unstructured":"Gajewski, H., Gr\u00f6ger, K., and Zacharias, K., Nichtlineare Operatorgleichungen und\nOperatordifferentialgleichungen, Berlin: Akademie-Verlag, 1974. Translated under the\ntitle: Nelineinye operatornye uravneniya i operatornye\ndifferentsial\u2019nye uravneniya, Moscow: Mir, 1978."},{"key":"2211_CR6","volume-title":"Funktsional\u2019nyi analiz (Functional Analysis)","author":"L.V. Kantorovich","year":"1984","unstructured":"Kantorovich, L.V. and Akilov, G.P., Funktsional\u2019nyi\nanaliz (Functional Analysis), Moscow: Nauka, 1984."},{"key":"2211_CR7","volume-title":"Uravneniya matematicheskoi fiziki. Dopolnitel\u2019nye glavy (Equations of Mathematical Physics. Additional Chapters)","author":"M.M. Karchevskii","year":"2012","unstructured":"Karchevskii, M.M. and Pavlova, M.F., Uravneniya matematicheskoi\nfiziki. Dopolnitel\u2019nye glavy (Equations of Mathematical Physics. Additional\nChapters), Kazan: Kazan. Gos. Univ., 2012."},{"key":"2211_CR8","first-page":"3","volume":"40","author":"M.O. Korpusov","year":"2006","unstructured":"Korpusov, M.O. and Sveshnikov, A.G., Blow-up of solutions of strongly\nnonlinear equations of the pseudoparabolic type, Sovrem. Mat.\nPril., 2006, vol. 40, pp. 3\u2013138.","journal-title":"Sovrem. Mat. Pril."},{"issue":"5","key":"2211_CR9","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1007\/s10625-005-0206-2","volume":"41","author":"M.O. Korpusov","year":"2005","unstructured":"Korpusov, M.O., Global solvability conditions for an initial-boundary value\nproblem for a nonlinear equation of pseudoparabolic type, Differ.\nEquations, 2005, vol. 41, no. 5, pp. 712\u2013720.","journal-title":"Differ. Equations"},{"issue":"12","key":"2211_CR10","first-page":"1765","volume":"43","author":"M.O. Korpusov","year":"2003","unstructured":"Korpusov, M.O. and Sveshnikov, A.G., Three-dimensional nonlinear evolution\nequations of pseudoparabolic type in problems of mathematical physics, Comput. Math. Math. Phys., 2003, vol. 43, no. 12,\npp. 1765\u20131797.","journal-title":"Comput. Math. Math. Phys."},{"key":"2211_CR11","volume-title":"Elementy funktsional\u2019nogo analiza (Elements of Functional Analysis)","author":"L.A. Lyusternik","year":"1965","unstructured":"Lyusternik, L.A. and Sobolev, V.I., Elementy funktsional\u2019nogo\nanaliza (Elements of Functional Analysis), Moscow:\nNauka, 1965."},{"key":"2211_CR12","unstructured":"Osipov, Yu.S., On the theory of differential games in systems with distributed\nparameters, Dokl. Akad. Nauk SSSR, 1975, vol. 223,\nno. 6, pp. 1314\u20131317."},{"key":"2211_CR13","volume-title":"Teoriya igr (Game Theory)","author":"L.A Petrosyan","year":"1998","unstructured":"Petrosyan, L.A, Zenkevich, N.A., and Semina, E.A., Teoriya\nigr (Game Theory), Moscow: Vyssh. Shkola, 1998."},{"issue":"5","key":"2211_CR14","doi-asserted-by":"publisher","first-page":"764","DOI":"10.1134\/S0001434615050119","volume":"97","author":"N.Yu. Satimov","year":"2015","unstructured":"Satimov, N.Yu. and Tukhtasinov, M., Evasion in a certain class of distributed\ncontrol systems, Math. Notes, 2015, vol. 97, no. 5,\npp. 764\u2013773.","journal-title":"Math. Notes"},{"issue":"1","key":"2211_CR15","first-page":"71","volume":"157","author":"S.V. Sokolov","year":"2004","unstructured":"Sokolov, S.V., On the solution of the problem of a differential game for\ndistributed dynamical systems, Probl. Upr. Inf., 2004,\nvol. 157, no. 1, pp. 71\u201377.","journal-title":"Probl. Upr. Inf."},{"issue":"7","key":"2211_CR16","first-page":"2083","volume":"28","author":"A.S. Furman","year":"1986","unstructured":"Furman, A.S., On the stratification of the space charge during transient\nprocesses in semiconductors, Fiz. Tverd. Tela, 1986,\nvol. 28, no. 7, pp. 2083\u20132090.","journal-title":"Fiz. Tverd. Tela"},{"key":"2211_CR17","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1134\/S0005117914040195","volume":"75","author":"A.V. Chernov","year":"2014","unstructured":"Chernov, A.V., On Volterra functional operator games on a given set,\nAutom. Remote Control, 2014, vol. 75,\npp. 787\u2013803.","journal-title":"Autom. Remote Control"},{"issue":"1","key":"2211_CR18","first-page":"74","volume":"4","author":"A.V. Chernov","year":"2012","unstructured":"Chernov, A.V., On existence of $$\\varepsilon\n$$-equilibrium in Volterra functional operator games\nwithout discrimination, Mat. Teoriya Igr. Pril., 2012,\nvol. 4, no. 1, pp. 74\u201392.","journal-title":"Mat. Teoriya Igr. Pril."},{"issue":"1","key":"2211_CR19","first-page":"316","volume":"19","author":"A.V. Chernov","year":"2013","unstructured":"Chernov, A.V., On $$\\varepsilon $$\n-equilibrium in noncooperative functional\u2013operator $$n\n$$-person games, Tr.\nInst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk, 2013, vol. 19, no. 1,\npp. 316\u2013328.","journal-title":"Tr. Inst. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk"},{"issue":"1","key":"2211_CR20","first-page":"91","volume":"6","author":"A.V. Chernov","year":"2014","unstructured":"Chernov, A.V., On existence of $$\\varepsilon\n$$-equilibrium in noncooperative $$n\n$$-person games associated with elliptic partial\ndifferential equations, Mat. Teoriya Igr. Pril., 2014,\nvol. 6, no. 1, pp. 91\u2013115.","journal-title":"Mat. Teoriya Igr. Pril."},{"issue":"3","key":"2211_CR21","first-page":"48","volume":"7","author":"A.V. Chernov","year":"2015","unstructured":"Chernov, A.V., On existence of the Nash equilibrium in a differential game\nassociated with elliptic equations: the monotone case, Mat. Teoriya\nIgr Pril., 2015, vol. 7, no. 3, pp. 48\u201378.","journal-title":"Mat. Teoriya Igr Pril."},{"issue":"5","key":"2211_CR22","first-page":"810","volume":"56","author":"F.L. Chernous\u2019ko","year":"1992","unstructured":"Chernous\u2019ko, F.L., Boundary controls in distributed parameter systems,\nPrikl. Mat. Mekh., 1992, vol. 56, no. 5,\npp. 810\u2013826.","journal-title":"Prikl. Mat. Mekh."},{"key":"2211_CR23","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1137\/0323015","volume":"23","author":"L.D. Berkovitz","year":"1985","unstructured":"Berkovitz, L.D., The existence of value and saddle point in games of fixed\nduration, SIAM J. Control Optim., 1985, vol. 23,\npp. 172\u2013196.","journal-title":"SIAM J. Control Optim."},{"issue":"1","key":"2211_CR24","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s40840-017-0581-x","volume":"2(42)","author":"G. Ibragimov","year":"2019","unstructured":"Ibragimov, G., Alias, I.A., Waziri, U., and Ja\u2019afaru, A.B., Differential game of\noptimal pursuit for an infinite system of differential equations, Bull.\nMalays. Math. Sci. Soc., 2019, vol. 2(42), no. 1, pp. 391\u2013403.","journal-title":"Bull. Malays. Math. Sci. Soc."},{"issue":"5","key":"2211_CR25","first-page":"697","volume":"35","author":"V.A. Il\u2019in","year":"1999","unstructured":"Il\u2019in, V.A. and Tikhomirov, V.V., The wave equation with a boundary control\nat both endpoints and the complete vibration damping problem, Differ. Equations, 1999, vol. 35, no. 5,\npp. 697\u2013708.","journal-title":"Differ. Equations"},{"issue":"1","key":"2211_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/1030001","volume":"30","author":"J.-L. Lions","year":"1988","unstructured":"Lions, J.-L., Exact controllability, stabilization and perturbations for\ndistributed systems, SIAM Rev., 1988, vol. 30, no. 1,\npp. 1\u201368.","journal-title":"SIAM Rev."},{"key":"2211_CR27","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/s10957-008-9478-z","volume":"141","author":"M. Ramaswamy","year":"2009","unstructured":"Ramaswamy, M. and Shaiju, A.J., Construction of approximate saddle-point\nstrategies for differential games in a Hilbert space, J. Optim. Theory\nAppl., 2009, vol. 141, pp. 349\u2013370.","journal-title":"J. Optim. Theory Appl."},{"key":"2211_CR28","doi-asserted-by":"crossref","unstructured":"Roxin, E.O., Differential games with partial differential equations, in\nDiffer. Games Appl., Enschede: Proc. Workshop, 1977,\nLect. Notes Control Inf. Sci., vol. 3,\npp. 186\u2013204.","DOI":"10.1007\/BFb0009071"},{"key":"2211_CR29","doi-asserted-by":"publisher","first-page":"1234","DOI":"10.1063\/1.4756375","volume":"1479","author":"M. Troeva","year":"2012","unstructured":"Troeva, M., Existence of equilibrium point for noncooperative differential\ngame in Banach space, AIP Conf. Proc., 2012, vol. 1479,\npp. 1234\u20131237.","journal-title":"AIP Conf. Proc."}],"container-title":["Automation and Remote Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117921110151.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0005117921110151","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117921110151.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T22:32:31Z","timestamp":1773613951000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0005117921110151"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11]]},"references-count":29,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["2211"],"URL":"https:\/\/doi.org\/10.1134\/s0005117921110151","relation":{},"ISSN":["0005-1179","1608-3032"],"issn-type":[{"value":"0005-1179","type":"print"},{"value":"1608-3032","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11]]},"assertion":[{"value":"14 January 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 September 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 September 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 December 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}