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Representation of Solutions of Systems of Linear Differential Equations with Multiple Delays and Linear Parts Given by Nonpermutable Matrices

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In recent results on representation of the solutions of systems of delayed differential equations, the condition that the linear parts are given by pairwise permutable matrices was assumed. We show how this strong condition can be avoided and derive a representation of solutions of systems of differential equations with nonconstant coefficients and variable delays. The results are applied to a system with two constant delays. In addition, the nonexistence of blow-up solutions is proved for nonlinear systems.

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Authors and Affiliations

  1. Department of Mathematics, Analysis, and Numerical Mathematics, Faculty of Mathematics, Physics, and Informatics, Comenius University in Bratislava, Mlynská Dolina, 842 48, Bratislava, Slovak Republic

    M. Medved’

  2. Department of Mathematics, Analysis, and Numerical Mathematics, Faculty of Mathematics, Physics, and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovak Republic

    M. Pospíšil

  3. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovak Republic

    M. Medved’ & M. Pospíšil

Authors
  1. M. Medved’
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  2. M. Pospíšil
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Correspondence to M. Medved’.

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Published in Neliniini Kolyvannya, Vol. 19, No. 4, pp. 521–532, October–December, 2016.

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Medved’, M., Pospíšil, M. Representation of Solutions of Systems of Linear Differential Equations with Multiple Delays and Linear Parts Given by Nonpermutable Matrices. J Math Sci 228, 276–289 (2018). https://doi.org/10.1007/s10958-017-3620-0

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  • DOI: https://doi.org/10.1007/s10958-017-3620-0

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