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On the Unique Solvability of a Nonlocal Boundary-Value Problem for Systems of Loaded Hyperbolic Equations with Impulsive Actions

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Ukrainian Mathematical Journal Aims and scope

We consider a nonlocal boundary-value problem with impulsive actions for a system of loaded hyperbolic equations and establish the relationship between the unique solvability of this problem and the unique solvability of a family of two-point boundary-value problems with impulsive actions for the system of loaded ordinary differential equations by the method of introduction of additional functions. By the method of parametrization, we establish sufficient conditions for the existence of a unique solution to a family of two-point boundary-value problems with impulsive effects for a system of loaded ordinary differential equations. The algorithms of finding the solutions of these boundary-value problems are constructed. The conditions for the unique solvability of the nonlocal boundary-value problem for a system of loaded hyperbolic equations with impulsive actions are obtained. We also propose the numerical realization of the algorithms of the method of parametrization for the solution of the family of two-point boundary-value problems with impulsive actions for the system of loaded ordinary differential equations. The results are illustrated by specific examples.

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Authors and Affiliations

  1. Institute of Mathematics and Mathematical Simulation, Ministry of Education and Science of the Republic of Kazakhstan, Almaty, Kazakhstan

    A. T. Asanova, Zh. M. Kadirbaeva & É. A. Bakirova

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  1. A. T. Asanova
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  2. Zh. M. Kadirbaeva
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  3. É. A. Bakirova
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 8, pp. 1011–1029, August, 2017.

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Asanova, A.T., Kadirbaeva, Z.M. & Bakirova, É.A. On the Unique Solvability of a Nonlocal Boundary-Value Problem for Systems of Loaded Hyperbolic Equations with Impulsive Actions. Ukr Math J 69, 1175–1195 (2018). https://doi.org/10.1007/s11253-017-1424-5

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  • DOI: https://doi.org/10.1007/s11253-017-1424-5

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