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.
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.
