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Existence of linear Pfaff systems with lower characteristic set consisting of countably many segments in the space R 3

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Abstract

We prove the existence of a completely integrable Pfaff system ∂x/∂t i = A i (t)x, x ∈ R n , t = (t 1, t 2, t 3) ∈ R 3+ , i = 1, 2, 3, with infinitely differentiable bounded coefficient matrices and with lower characteristic set being the union of countably many segments in the space R 3.

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Authors and Affiliations

  1. Mogilev State University, Mogilev, Belarus

    A. S. Platonov & A. A. Timofeeva

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  1. A. S. Platonov
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  2. A. A. Timofeeva
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Additional information

Original Russian Text © A.S. Platonov, A.A. Timofeeva, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 10, pp. 1444–1452.

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Platonov, A.S., Timofeeva, A.A. Existence of linear Pfaff systems with lower characteristic set consisting of countably many segments in the space R 3 . Diff Equat 46, 1448–1456 (2010). https://doi.org/10.1134/S0012266110100083

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  • DOI: https://doi.org/10.1134/S0012266110100083

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