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Exact differential equations over matrix skew series

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Abstract

In this paper we establish sufficient conditions for the reducibility of first-order matrix differential equations stated in terms of differentials to exact scalar differential equations.

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References

  1. Petrovskii, I. G. Lectures on the Theory of Ordinary Differential Equations (Nauka, Moscow, 1970).

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  2. Derevenskii, V. P. “Quadratic Equations Over Matrix Skew Series,” Russian Mathematics (Iz. VUZ) 58, No. 1, 14–26 (2014).

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  3. Jacobson, N. Lie Algebras (John Wiley and Sons, New York-London, 1962; Mir, Moscow, 1964).

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  4. Zautsev, V. F., Polyanin, A. D. Handbook of Ordinary Differential Equations (Fizmatlit, Moscow, 2001) [in Russian].

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  5. Derevenskii, V. P. “Hyperbolic Functions and First Order Nonlinear Ordinary Differential Equations Over a Banach Algebra,” Russian Mathematics (Iz. VUZ) 50, No. 8, 5–16 (2006).

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Authors and Affiliations

  1. Kazan State Architecture and Building University, ul. Zelyonaya 1, Kazan, 420043, Russia

    V. P. Derevenskii

Authors
  1. V. P. Derevenskii
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Correspondence to V. P. Derevenskii.

Additional information

Original Russian Text © V.P. Derevenskii, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 3, pp. 49–62.

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Derevenskii, V.P. Exact differential equations over matrix skew series. Russ Math. 59, 43–54 (2015). https://doi.org/10.3103/S1066369X15030056

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  • DOI: https://doi.org/10.3103/S1066369X15030056

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