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Nonlocal boundary-value problem for linear partial differential equations unsolved with respect to the higher time derivative

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Abstract

We study the well-posedness of the problem with general nonlocal boundary conditions in the time variable and conditions of periodicity in the space coordinates for partial differential equations unsolved with respect to the higher time derivative. We establish the conditions of existence and uniqueness of the solution of the considered problem. In the proof of existence of the solution, we use the method of divided differences. We also prove metric statements on the lower bounds of small denominators appearing in constructing the solution of the problem.

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Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv

    O. D. Vlasii & B. I. Ptashnyk

Authors
  1. O. D. Vlasii
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  2. B. I. Ptashnyk
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__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 3, pp. 370–381, March, 2007.

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Vlasii, O.D., Ptashnyk, B.I. Nonlocal boundary-value problem for linear partial differential equations unsolved with respect to the higher time derivative. Ukr Math J 59, 409–422 (2007). https://doi.org/10.1007/s11253-007-0026-z

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  • DOI: https://doi.org/10.1007/s11253-007-0026-z

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