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Method of Local Linear Approximation in the Theory of Nonlinear Impulsive Systems

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Ukrainian Mathematical Journal Aims and scope

For nonlinear differential equations with impulsive perturbations, we formulate a general assertion concerning the existence of bounded solutions. By using this assertion, we establish necessary and sufficient conditions for the existence and uniqueness of bounded solutions of analogous linear equations. For the investigation of equations, we use the theory of c-continuous operators and the method of local linear approximation of nonlinear equations.

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Authors and Affiliations

  1. T. Shevchenko Kyiv National University, Kyiv, Ukraine

    M. O. Perestyuk

  2. Management and Utilization of Natural Resources, National University of Water, Rivne, Ukraine

    V. Yu. Slyusarchuk

Authors
  1. M. O. Perestyuk
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  2. V. Yu. Slyusarchuk
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Correspondence to V. Yu. Slyusarchuk.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, No. 1, pp. 105–120, January, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i1.7347.

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Perestyuk, M.O., Slyusarchuk, V.Y. Method of Local Linear Approximation in the Theory of Nonlinear Impulsive Systems. Ukr Math J 75, 118–137 (2023). https://doi.org/10.1007/s11253-023-02189-4

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  • DOI: https://doi.org/10.1007/s11253-023-02189-4

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