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Boundary-value problems for differential equations unsolvable with respect to the higher time derivative

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Abstract

For differential equations with constant coefficients unsolvable with respect to the higher time derivative, we establish conditions of the existence and uniqueness of solutions of problems with conditions local in time and periodic in space variables. We prove a metric theorem on lower bounds of small denominators appearing in the construction of solutions of the problems.

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Author information

Authors and Affiliations

  1. Lvov University, Lvov

    L. I. Komarnitskaya

  2. Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, Lvov

    B. I. Ptashnik

Authors
  1. L. I. Komarnitskaya
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  2. B. I. Ptashnik
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 9, pp. 1197–1208, September, 1995.

This work was supported by the Foundation for Fundamental Research of the Ukrainian State Committee on Science and Technology.

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Komarnitskaya, L.I., Ptashnik, B.I. Boundary-value problems for differential equations unsolvable with respect to the higher time derivative. Ukr Math J 47, 1364–1377 (1995). https://doi.org/10.1007/BF01057511

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  • DOI: https://doi.org/10.1007/BF01057511

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