The subspace of space of almost periodic vector-functions are found, in which the problem about branching of almost periodic solutions of ordinary differential equations with small parameter is investigated by the help theory of Lyapunov–Shmidt. The nonlocal theorems of existence of almost periodic solutions of ordinary differential equations are obtained. The problem about bifurcation of almost periodic solutions from steady of equilibrium are investigated in case of one-dimensional degeneration The principle of averaging was justified for functional-differential equations without supposition of smallness delay. The principle of averaging was justified for quasiconservative vibro-impact system. The averaging technique was developed for calculation resonance solutions in such systems. A new method of asymptotic integration of linear differential equations with oscillatory decreasing coefficients was developed.
Biography
Graduated from Faculty of Mathematics and Mechanics of Kiev State University in 1961 (department of mathematical analysis). Ph.D. thesis was defended in 1966. A list of my works contains more than 100 titles.
Main publications:
Burd V. Sh. K zadache o razvetvlenii pochti periodicheskikh reshenii nekotorykh sistem differentsialnykh uravnenii // DAN SSSR, 1964, 159, # 2, 239–242.
Krasnoselskii M. A., Burd V. Sh., Kolesov Yu. S. Nelineinye pochti periodicheskie kolebaniya. M.: Nauka, 1970. 352 s.
Burd V. Sh. Resonant almost periodic oscillations in systems with slow varying parameters // International Journal Non-Linear Mechanics, 1997, 32, no. 6, 1143–1152.
Burd V. Sh., Karakulin V. A. Asimptoticheskoe integrirovanie sistem lineinykh differentsialnykh uravnenii s kolebatelno ubyvayuschimi koeffitsientami // Matematicheskie zametki, 1998, 64, # 5, 658–666.
Burd V. Sh., Krupenin V. L. On the calculation of resonance oscillations of the vibro-impact systems by the averaging technique // Dynamics of Vibro-Impact Systems, Proceedings of the Euromech Colloquium 15–18 September 1998, Springer, 1999, 127–135.
V. Sh. Burd, “About the works by Yu. S. Kolesov on differential equations”, Model. Anal. Inform. Sist., 16:3 (2009), 5–12
2007
2.
V. Sh. Burd, “О работах А. Ю. Левина по теории линейных дифференциальных уравнений”, Model. Anal. Inform. Sist., 14:3 (2007), 4–7
1998
3.
V. Sh. Burd, V. A. Karakulin, “On the asymptotic integration of systems of linear differential equations with oscillatory decreasing coefficients”, Mat. Zametki, 64:5 (1998), 658–666; Math. Notes, 64:5 (1998), 571–578
V. Sh. Burd, “Stability of solutions of some classes of linear differential equations with oscillating coefficients”, Differ. Uravn., 19:8 (1983), 1450–1452
1970
5.
V. Sh. Burd, Yu. S. Kolesov, “The dichotomy of solutions of functional differential equations with almost periodic coefficients”, Dokl. Akad. Nauk SSSR, 195:6 (1970), 1259–1262
6.
V. Sh. Burd, Yu. S. Kolesov, M. A. Krasnosel'skii, “The bifurcation of the almost periodic solutions of singularly perturbed differential equations”, Uspekhi Mat. Nauk, 25:1(151) (1970), 189–190
1969
7.
V. Sh. Burd, P. P. Zabreiko, Yu. S. Kolesov, M. A. Krasnosel'skii, “The averaging principle and bifurcation of almost periodic solutions”, Dokl. Akad. Nauk SSSR, 187:6 (1969), 1219–1221
8.
V. Sh. Burd, Yu. S. Kolesov, M. A. Krasnosel'skii, “On the existence and constancy of sign of Green's function of scalar equations of high order with almost periodic coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 33:6 (1969), 1399–1415; Math. USSR-Izv., 3:6 (1969), 1319–1334
9.
V. Sh. Burd, Yu. S. Kolesov, M. A. Krasnosel'skii, “Investigation of the Green's function for differential operators with almost periodic coefficients”, Izv. Akad. Nauk SSSR Ser. Mat., 33:5 (1969), 1089–1119; Math. USSR-Izv., 3:5 (1969), 1027–1054
V. Sh. Burd, T. Sabirov, “The stability of branching almost periodic solutions of certain systems of differential equations”, Dokl. Akad. Nauk SSSR, 176:5 (1967), 991–993
1964
11.
V. Sh. Burd, “On the branching of almost periodic solutions of nonlinear ordinary differential equations”, Dokl. Akad. Nauk SSSR, 159:2 (1964), 239–242
1998
12.
E. A. Asarin, I. A. Bakhtin, N. A. Bobylev, V. A. Bondarenko, V. Sh. Burd, E. A. Gorin, S. V. Emel'yanov, P. P. Zabreiko, L. A. Ivanov, V. S. Kozyakin, A. M. Krasnosel'skii, N. A. Kuznetsov, A. B. Kurzhanskii, A. Yu. Levin, È. M. Muhamadiev, A. I. Perov, Yu. V. Pokornyi, A. V. Pokrovskii, D. I. Rachinskii, V. V. Strygin, Ya. Z. Tsypkin, V. V. Chernorutski, “Memory of M. A. Krasnosel'skii”, Avtomat. i Telemekh., 1998, no. 2, 179–184
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