Pacific national university Main page Bulletin of Pacific national university

UDC 517.91, 519.21

© E. V. Karachanskaya, 2011

CONSTRUCTION OF THE FULL SET OF THE DIFFERENTIAL EQUATION SYSTEMS WITH PRESCRIBED FIRST INTEGRAL COLLECTION

A new construction algorithm for the set of the diffrrential equation (ordinary and stochastic) systems is proposed. For which the prescribed set of independent functions presents the set of the first integrals. We prove that the set of the diffrrential equation systems is full.

Keywords: the first integral, ordinary diffrrential equation, stochastic diffrrential equation, algorithm of the construction.

References:

  1. Dubko V. A. Voprosy teorii i primeneniya stokhasticheskikh differentsialnykh uravneniy. - Vladivostok: DVO AN SSSR, 1989. - 185 c.
  2. Dubko V. A. Pervyy integral sistemy stokhasticheskikh differentsialnykh uravneniy: priprint. - Kiev : AN USSR, In-t matematiki, 1978. - 22 s.
  3. Erugin N. P. Postroenie vsego mnozhestva differentsialnykh uravneniy, imeyushchikh zadannuyu integral`nuyu krivuyu. PMM, T.16, 1952, vyp.6, S. 659-670.
  4. Elsgolts L. E. Differentsialnye uravneniya i variatsionnoe ischislenie. -- M.: Nauka, 1969. -- 424 s.
  5. Chalykh, E. V. Constructing the set of program controls with probability 1 for one class of stochastic systems // Automation and Remote Control. -- 2009. – Vol. 70,  ¹ 8. – Ð. 1164-1375.
  6. Karachanskaya E. V. Postroenie mnozhestva differentsialnykh uravneniy, obladayushchikh zadannym naborom pervykh integralov: preprint ¹ 152 Vychislitel`nyy tsentr DVO RAN / Habarovsk : Izd-vo Tikhookean. gos. un-ta, 2010. - 19 s.
  7. Chalykh, E. V. On one generalization of the Langevin equation with determinate modulus of velocity // Ukr. Math. J.. -- 1998. – Vol. 50, ¹ 7. --P. 1145-1147.
  8. Nikolskiy S. M. Kurs matematicheskogo analiza, T.1., 3-e izd., pererab. i dop. -- M.: Nauka, Glav. red. fiz.-mat. lit., 1983. -- 464 c.
  9. V poiskakh skrytogo poryadka (Metodologicheskie problemy izucheniya regiona)/ V. A. Dubko, F. N. Ryanskiy, E. M. Soroko, V. N. Sholpo, V. V. YUshmanov. - Vladivostok: Dalnauka, 1995. - 118 s.

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