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On the expansion of solutions to differential equations with discontinuous right-hand side in a series in initial data and parameters

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Abstract

The conditions under which the solutions of equations with discontinuous right-hand sides depend on the initial data and parameters analytically are investigated. A definition is introduced, which specifies this dependence in the case where a surface of discontinuity exists.

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References

  1. A. M. Samoilenko, N. A. Perestyuk, and M. U. Akhmetov,Differential Properties of Solutions and Integral Surfaces for Nonlinear Pulse Systems [in Russian], Preprint No. 90.37, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1990).

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  4. A. F. Filippov,Differential Equations with Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1985).

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Authors and Affiliations

  1. Kiev University, Kiev

    M. U. Akhmetov

Authors
  1. M. U. Akhmetov
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 5, pp. 715–717, May, 1993.

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Akhmetov, M.U. On the expansion of solutions to differential equations with discontinuous right-hand side in a series in initial data and parameters. Ukr Math J 45, 786–789 (1993). https://doi.org/10.1007/BF01058213

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  • DOI: https://doi.org/10.1007/BF01058213

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