Abstract
In this paper, we find sufficient conditions for the solvability by quadratures of J. Bernoulli’s equation defined over the set M 2 of square matrices of order 2. We consider the cases when such equations are stated in terms of bases of a two-dimensional abelian algebra and a three-dimensional solvable Lie algebra over M 2. We adduce an example of the third degree J. Bernoulli’s equation over a commutative algebra.
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V.P. Derevenskii, “Matrix Bernoulli Equations. I,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 2, 14–23 (2008) [Russian Mathematics (Iz. VUZ) 52 (2), 12–21 (2008)].
J.-P. Serre, Lie Algebras and Lie Groups (Benjamin, NY, 1965; Mir, Moscow, 1969).
A. Z. Petrov, Einstein Spaces (GIFML, Moscow, 1961) [in Russian].
V. P. Derevenskii, “Matrix Linear Differential Equations of Higher Order,” Differents. Uravneniya 29(4), 711–714 (1993).
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Original Russian Text © V.P. Derevenskii, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 7, pp. 3–10.
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Derevenskii, V.P. Matrix Bernoulli equations. II. Russ Math. 52, 1–7 (2008). https://doi.org/10.3103/S1066369X08070013
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DOI: https://doi.org/10.3103/S1066369X08070013