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Closed irregularity sets of linear differential systems with a parameter multiplying the derivative

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Abstract

For any closed subset M of the real line that does not contain zero, we construct a linear differential system with bounded piecewise continuous coefficient matrix A(·) such that the corresponding system with coefficient matrix µA(·) linearly depending on a real parameter µ is Lyapunov irregular for all µ in M and Lyapunov regular for all other parameter values.

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Authors and Affiliations

  1. Institute for Mathematics, National Academy of Science, Minsk, Belarus

    A. V. Lipnitskii

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  1. A. V. Lipnitskii
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Original Russian Text © tA.V. Lipnitskii, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 2, pp. 189–194.

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Lipnitskii, A.V. Closed irregularity sets of linear differential systems with a parameter multiplying the derivative. Diff Equat 47, 187–192 (2011). https://doi.org/10.1134/S0012266111020054

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  • DOI: https://doi.org/10.1134/S0012266111020054

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