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Representation of a solution of the Cauchy problem for an oscillating system with pure delay

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Nonlinear Oscillations

Abstract

We obtain a representation of a solution of the Cauchy problem for a linear inhomogeneous differential equation with constant coefficients and pure delay. We use special matrix functions called a delayed matrix sine and a delayed matrix cosine. They have the form of matrix polynomials of degree dependent on the value of delay.

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Authors and Affiliations

  1. Shevchenko Kiev National University, Kiev, Ukraine

    D. Ya. Khusainov

  2. Žilina University, Žilina, Slovakia

    J. Diblík, M. Růžičková & J. Lukáčová

Authors
  1. D. Ya. Khusainov
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  2. J. Diblík
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  3. M. Růžičková
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  4. J. Lukáčová
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Corresponding author

Correspondence to J. Diblík.

Additional information

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Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 261–270, April–June, 2008.

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Khusainov, D.Y., Diblík, J., Růžičková, M. et al. Representation of a solution of the Cauchy problem for an oscillating system with pure delay. Nonlinear Oscill 11, 276–285 (2008). https://doi.org/10.1007/s11072-008-0030-8

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  • DOI: https://doi.org/10.1007/s11072-008-0030-8

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