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Integral manifolds of systems of differential equations with a random right-hand side in a Banach space

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Abstract

The concept of an integral manifold of a system of differential equations with a random right-hand side is introduced. The problem of the existence of an integral manifold of a certain class of differential equations in a Banach space and several of its properties are investigated.

Literature cited

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    N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1974).

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    Yu. A. Mitropolskii and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics [in Russian], Nauka, Moscow (1973).

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    O. B. Lykova, “Integral manifolds of nonlinear differential equations in a Banach space,” in: Proceedings of V International Conference on Nonlinear Oscillations, Vol. 1, Analytic Methods [in Russian], Izd. Akad. Nauk UkrSSR, Kiev (1970), pp. 375–379.

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    A. I. Mel'nikov, “On stochastic integral manifolds of systems of differential equations with random parameters,” in: On Investigation of Certain Nonlinear Differential Systems with Random Parameters [in Russian], pp. 18–34, Preprint 88.19, Akad. Nauk UkrSSR, Inst. Mat., Kiev (1988).

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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 1, pp. 17–21, January, 1992.

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Kolomiets, V.G., Mel'nikov, A.I. Integral manifolds of systems of differential equations with a random right-hand side in a Banach space. Ukr Math J 44, 12–16 (1992). https://doi.org/10.1007/BF01062623

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Keywords

  • Differential Equation
  • Banach Space
  • Integral Manifold