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On the smoothness of solutions of differential equations with a discontinuous right-hand side

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Ukrainian Mathematical Journal Aims and scope

Abstract

A method for the investigation of differential equations with a nonclassical right-hand side [1] is applied to the study of the higher-order differentiability of solutions of differential equations with discontinuous right-hand sides with respect to the initial data. We use results from the theory of differential equations with pulse influence [2].

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References

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

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  2. A. M. Samoilenko and N. A. Perestyuk,Differential Equations with Pulse Influence [in Russian], Vyshcha Shkola, Kiev (1987).

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  3. 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

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  1. M. U. Akhmetov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1587–1594, December, 1993.

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Akhmetov, M.U. On the smoothness of solutions of differential equations with a discontinuous right-hand side. Ukr Math J 45, 1785–1792 (1993). https://doi.org/10.1007/BF01061348

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  • DOI: https://doi.org/10.1007/BF01061348

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