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On the structure of the general solution and conditions of solvability of the Cauchy problem for degenerate linear systems of higher-order differential equations

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Ukrainian Mathematical Journal Aims and scope

For a system of linear differential equations of order p with identically degenerate coefficient matrix of higher derivatives, we establish conditions under which this system has the general solution of the Cauchy type. The structure of this solution is determined. Conditions for the existence and uniqueness of solution of the corresponding initial-value problem are also obtained.

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References

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Authors and Affiliations

  1. Drahomanov National Pedagogic University, Kyiv, Ukraine

    S. P. Pafyk

  2. University of Management of Education of the Ukrainian National Academy of Pedagogic Sciences, Kyiv, Ukraine

    V. P. Yakovets’

Authors
  1. S. P. Pafyk
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  2. V. P. Yakovets’
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Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 2, pp. 296–306, February, 2013.

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Pafyk, S.P., Yakovets’, V.P. On the structure of the general solution and conditions of solvability of the Cauchy problem for degenerate linear systems of higher-order differential equations. Ukr Math J 65, 328–340 (2013). https://doi.org/10.1007/s11253-013-0780-z

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  • DOI: https://doi.org/10.1007/s11253-013-0780-z

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