Юрий Филиппович Долгий (2 августа 1947, Вставское) — доктор физико-математических наук, профессор, доцент, автор более 100 научных работ.

В 1970 году окончил Уральский государственный университет по специальности «Механика», в дальнейшем стал работать на кафедре теоретической механики математико-механического факультета университета. Прочитал курсы по теоретической механике, дифференциальным уравнениям, теории устойчивости движений, теории нелинейных колебаний и теории автоматического регулирования.

Биография Родился 2 августа 1947 года в Вставском Омской области.

В 1970 году окончил УрГУ по специальности «Механика», в дальнейшем стал работать на кафедре теоретической механики математико-механического факультета университета. Прочитал курсы по теоретической механике, дифференциальным уравнениям, теории устойчивости движений, теории нелинейных колебаний и теории автоматического регулирования.

Юрий Филиппович принадлежит к научной школе профессора С. Н. Шиманова. Его областью научных интересов является качественная теория дифференциальных уравнений с последействием. Основные научные результаты связаны с развитием первого метода Ляпунова и метода бифуркаций при исследовании устойчивости периодических движений. Является автором более 100 научных работ, подготовил шесть кандидатов наук. Удостоен первой премии УрГУ в 1996 году за цикл научных работ по теории устойчивости периодических движений динамических систем с последействием. Почетный работник высшего профессионального образования Российской Федерации с 2003 года.

Основные труды

Dolgii, Yu. F.; Surkov, P. G. A variational approach towards solving an ill-posed Cauchy problem for a functional-differential equation. (English) Zbl 1364.34092 Funkc. Ekvacioj, Ser. Int. 59, No. 2, 157—183 (2016). MSC: 34K06 47A52 58E50 Dolgii, Yurii F.; Surkov, Platon G. Ill-posed problem of reconstruction of the population size in the Hutchinson-Wright equation. (English) Zbl 06920136 Ural Math. J. 1, No. 1, 30-44 (2015). MSC: 34 65 Dolgii, Yu. F.; Koshkin, E. V. Stabilization of periodic systems with aftereffect by finite-dimensional approximations. (English. Russian original) Zbl 1317.93210 Russ. Math. 59, No. 1, 24-38 (2015); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2015, No. 1, 29-45 (2015). MSC: 93D15 93C15 34C26 Dolgii, Yu. F.; Surkov, P. G. Asymptotics of regularized solutions of an ill-posed Cauchy problem for an autonomous linear system of differential equations with commensurable delays. (English. Russian original) Zbl 1376.34060 Proc. Steklov Inst. Math. 287, Suppl. 1, S55-S67 (2014); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 19, No. 4, 107—118 (2013). MSC: 34K05 34K06 Dolgii, Yu. F.; Bykov, D. S. Linear functional differential equations in space with unindefinite metric. (Russian. English summary) Zbl 1305.34107 Izv. Inst. Mat. Inform., Udmurt. Gos. Univ. 2012, No. 1(39), 48-49 (2012). MSC: 34K06 34K20 Bykov, D. S.; Dolgii, Yu. F. Approximating characteristic equations for autonomous systems of differential equations with aftereffect. (English. Russian original) Zbl 1235.34177 Russ. Math. 55, No. 1, 7-18 (2011); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2011, No. 1, 10-23 (2011). Reviewer: Wing-Sum Cheung (Hong Kong) MSC: 34K08 34K06 Dolgii, Yu. F.; Surkov, P. G. Asymptotics of regularized solutions of a linear nonautonomous system of advanced differential equations. (English. Russian original) Zbl 1215.34073 Differ. Equ. 46, No. 4, 470—488 (2010); translation from Differ. Uravn. 46, No. 4, 467—485 (2010). Reviewer: Hong Zhang (Zhenjiang) MSC: 34K06 34K25 Dolgii, Yu. F.; Nidchenko, S. N. Analysis of a mathematical predator-prey model with delay. (English. Russian original) Zbl 1181.34087 Differ. Equ. 44, No. 6, 861—865 (2008); translation from Differ. Uravn. 44, No. 6, 837—840 (2008). Reviewer: Klaus R. Schneider (Berlin) MSC: 34K60 34K13 92D25 Dolgii, Yu. F.; Kukushkina, E. V. Construction of the approximate characteristic equations for autonomous systems of functional-difference equations. (English) Zbl 1148.34051 Funct. Differ. Equ. 15, No. 3-4, 183—198 (2008). MSC: 34K20 34K06 34K28 Dolgii, Yu. F.; Ul’yanov, E. V. Singular numbers of the monodromy operator and sufficient conditions of the asymptotic stability of periodic system of differential equations with fixed delay. (English. Russian original) Zbl 1238.34138 Proc. Steklov Inst. Math. 259, Suppl. 2, S95-S110 (2007); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 13, No. 2 (2007). MSC: 34K20 34K06 Dolgii, Yu. F. Stabilization of linear autonomous systems of differential equations with distributed delay. (English. Russian original) Zbl 1146.93032 Autom. Remote Control 68, No. 10, 1813—1825 (2007); translation from Avtom. Telemekh. 2007, No. 10, 92-105 (2007). MSC: 93D15 93C15 93C05 Dolgii, Yu. F.; Ul’yanov, E. V. Sufficient conditions for exponential stability of a periodic system with multiple delays. (Russian) Zbl 1196.34097 Izv. Ural. Gos. Univ. 44, Mat. Mekh. 9, 54-75 (2006). MSC: 34K20 Dolgiĭ, Yu. F. Asymptotics of characteristic exponents for functional-differential equations. (Russian. English summary) Zbl 1191.34095 Izv. Ural. Gos. Univ. 46, Mat. Mekh. 10, 50-59 (2006). MSC: 34K25 34K06 34D08 Dolgii, Yu. F. Application of self-adjoint boundary value problems to investigation of stability of periodic delay systems. (English) Zbl 1130.34049 Osipov, Yu. S. (ed.), Control, stability, and inverse problems of dynamics. Transl. from the Russian. Moscow: Maik Nauka/Interperiodica, Pleiades Publishing/distrib. by Springer. Proceedings of the Steklov Institute of Mathematics 2006, Suppl. 2, S16-S25 (2006). Reviewer: Ivan Ginchev (Varese) MSC: 34K20 34K06 Dolgy, Yu. F.; Nidchenko, S. N. Stability of antisymmetric periodic solutions for differential equations with delay. (Russian. English summary) Zbl 1180.34074 Izv. Ural. Gos. Univ. 38, Mat. Mekh. 8, 50-68 (2005). MSC: 34K13 34K20 Dolgii, Yu. F.; Zakharov, A. V. Periodic oscillations in conservative systems with a small delay. (English. Russian original) Zbl 1148.34325 Differ. Equ. 41, No. 10, 1367—1378 (2005); translation from Differ. Uravn. 41, No. 10, 1299—1309 (2005). Reviewer: Xinyu Song (Xinyang) MSC: 34K13 34D10 Dolgii, Yu. F. Characteristic equation in the problem of asymptotic stability in periodic systems with aftereffect. (English) Zbl 1131.34318 Gusev, M. I. (ed.), Dynamical systems and control problems. Transl. from the Russian. Moscow: Maik Nauka/Interperiodica. Proceedings of the Steklov Institute of Mathematics 2005, Suppl. 1, S82-S94 (2005). Reviewer: Ivan Ginchev (Varese) MSC: 34K06 93D20 34K20 Dolgii, Yu. F.; Nidchenko, S. N. A branching method for studying stability of a solution to a delay differential equation. (Russian, English) Zbl 1122.34046 Sib. Mat. Zh. 46, No. 6, 1288—1301 (2005); translation in Sib. Math. J. 46, No. 6, 1039—1049 (2005). MSC: 34K13 34K20 34K18 34C25 Dolgiĭ, Yu. F. Shimanov’s method of auxiliary systems in the problem of constructing bifurcation equations. (Russian. English summary) Zbl 1179.34036 Izv. Ural. Gos. Univ. 26, Mat. Mekh. 5, 55-65, 191 (2003). MSC: 34C23 34C25 34K13 34K18 Dolgii, Yu. F.; Zakharov, A. V. A delay effect upon periodic oscillations in a conservative system. (English) Zbl 1127.34342 Vasil’eva, E. V. (ed.), Fluid dynamics. Transl. from the Russian. Moscow: Maik Nauka/Interperiodica. Proceedings of the Steklov Institute of Mathematics 2003, Suppl. 2, S24-S44 (2003). MSC: 34K20 34K13 Dolgiĭ, Yu. F.; Kukrushkina, E. V. The general form of solution of a linear nonstationary system of functional-difference equation. (English. Russian original) Zbl 1075.39009 Russ. Math. 47, No. 7, 25-33 (2003); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2003, No. 7, 27-34 (2003). MSC: 39A12 34K12 Dolgiĭ, Yu. F.; Tarasyan, V. S. Conditions for finite-dimensionality of a monodromy operator for periodic sytems with aftereffect. (English. Russian original) Zbl 1086.34056 Russ. Math. 47, No. 4, 24-36 (2003); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2003, No. 4, 27-39 (2003). Reviewer: Rui Xu (Shijiazhuang) MSC: 34K06 47N20 Dolgij, Yu. F.; Kukushkina, E. V. Representations of solutions of stationary functional-difference equations. (Russian. English summary) Zbl 1034.39015 Izv. Ural. Gos. Univ. 22, Mat. Mekh. 4, 62-80 (2002). MSC: 39B42 39B99 Dolgiĭ, Yu. F.; Blizorukov, M. G. Dynamic systems in an economy with discrete time. (Russian) Zbl 1075.91600 Ehkon. Mat. Metody 38, No. 3, 94-106 (2002). MSC: 91B62 Blizorukov, M. G.; Dolgij, Yu. F. Periodic solutions of a system of linear difference equations with continuous argument. (English. Russian original) Zbl 1033.39005 Differ. Equ. 37, No. 4, 568—577 (2001); translation from Differ. Uravn. 37, No. 4, 538—546 (2001). MSC: 39A11 39A10 Dolgij, Yu. F.; Nikolaev, S. G. Stability of a periodic solution to a nonlinear delay differential equation. (English. Russian original) Zbl 0999.34071 Differ. Equ. 37, No. 5, 621—630 (2001); translation from Differ. Uravn. 37, No. 5, 592—600 (2001). Reviewer: Alexander Olegovich Ignatyev (Donetsk) MSC: 34K20 34K13 Dolgij, Yu. F.; Tarasyan, V. S. Finite-dimensional monodromy operators for periodic systems of differential equations with aftereffect. (Russian. English summary) Zbl 0996.34051 Izv. Ural. Gos. Univ. 18, Mat. Mekh. 3, 67-83 (2000). Reviewer: Victor I.Tkachenko (Kyïv) MSC: 34K06 34M35 34K05 Dolgii, Yu. F.; Nikolaev, S. G. On the stability of a periodic system of delay differential equations. (English. Russian original) Zbl 0997.34068 Differ. Equations 35, No. 10, 1346—1352 (1999); translation from Differ. Uravn. 35, No. 10, 1330—1336 (1999). Reviewer: Stieg Olof Londen (Espoo) MSC: 34K20 34K25 34K06 Dolgiǐ, Yu. F. The characteristic equation for the stability problem of periodic systems with aftereffect. (Russian. English summary) Zbl 0978.34062 Izv. Ural. Gos. Univ. 10, Mat. Mekh. 1, 34-43 (1998). MSC: 34K20 34L05 34K30 Dolgij, Yu. F.; Nikolaev, S. G. Instability of a periodic delay system. (English. Russian original) Zbl 0974.34073 Differ. Equations 34, No. 4, 463—468 (1998); translation from Differ. Uravn. 34, No. 4, 465—470 (1998). Reviewer: Valentin Chernyatin (Szczecin) MSC: 34K20 34K06 Dolgij, Yu. F.; Plastinin, N. V. Asymptotics of eigenvalues of the monodromy operator for a differential equation of neutral type with periodic coefficients. (English. Russian original) Zbl 0901.34071 Differ. Equations 32, No. 11, 1554—1557 (1996); translation from Differ. Uravn. 32, No. 11, 1558—1560 (1996). Reviewer: V.Chernyatin (Szczecin) MSC: 34K25 34K40 Dolgij, Yu. F. Infinite realizations of an «input-output» mapping with continuous time. (English. Russian original) Zbl 0857.93021 J. Comput. Syst. Sci. Int. 34, No. 1, 103—109 (1996); translation from Izv. Ross. Akad. Nauk, Tekh. Kibern. 1994, No. 4, 190—197 (1994). Reviewer: B.F.Šmarda (Brno) MSC: 93B15 93C25 Dolgij, Yu. F. Asymptotics of eigenvalues of the monodromy operator for periodic differential equations with delay. (English. Russian original) Zbl 0836.34085 Russ. Math. 38, No. 11, 17-25 (1994); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1994, No. 11 (390), 20-28 (1994). Reviewer: W.Müller (Berlin) MSC: 34K25 34K13 34K20 Dolgij, Yu. F. Representation of the monodromy operator as the sum of a finite- dimensional operator and a Volterra operator. (English. Russian original) Zbl 0836.34066 Russ. Acad. Sci., Dokl., Math. 49, No. 1, 43-46 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 334, No. 2, 138—140 (1994). Reviewer: J.Banaś (Rzeszów) MSC: 34K05 45D05 47B10 34L20 Dolgij, Yu. F.; Putilova, E. N. Backward extension of solutions to a linear delay differential equation as an ill-posed problem. (English. Russian original) Zbl 0808.34071 Differ. Equations 29, No. 8, 1141—1146 (1993); translation from Differ. Uravn. 29, No. 8, 1317—1323 (1993). Reviewer: T.Dłotko (Katowice) MSC: 34K05