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Problems for partial differential equations with nonlocal conditions. Metric approach to the problem of small denominators

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Ukrainian Mathematical Journal Aims and scope

Abstract

A survey of works of the authors and their disciples devoted to the investigation of problems with nonlocal conditions with respect to a selected variable in cylindrical domains is presented. These problems are considered for linear equations and systems of partial differential equations that, in general, are ill posed in the Hadamard sense and whose solvability in certain scales of functional spaces is established for almost all (with respect to Lebesgue measure) vectors composed of the coefficients of the problem and the parameters of the domain.

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Authors and Affiliations

  1. “L’vivs’ka Politekhnika” National University, Lviv

    V. S. Il’kiv

  2. Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv

    B. I. Ptashnyk

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  1. V. S. Il’kiv
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  2. B. I. Ptashnyk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1624–1650, December, 2006.

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Il’kiv, V.S., Ptashnyk, B.I. Problems for partial differential equations with nonlocal conditions. Metric approach to the problem of small denominators. Ukr Math J 58, 1847–1875 (2006). https://doi.org/10.1007/s11253-006-0172-8

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