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Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Variable Coefficients

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Ukrainian Mathematical Journal Aims and scope

Abstract

We establish conditions for the unique solvability of a boundary-value problem for a weakly nonlinear hyperbolic equation of order 2n, n > (3p + 1)/2, with coefficients dependent on the space coordinates and data given on the entire boundary of a cylindric domain \(D \subset \mathbb{R}^{p + 1}\). The investigation of this problem is connected with the problem of small denominators.

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Authors and Affiliations

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

    N. I. Bilusyak & B. I. Ptashnyk

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  1. N. I. Bilusyak
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  2. B. I. Ptashnyk
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Bilusyak, N.I., Ptashnyk, B.I. Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Variable Coefficients. Ukrainian Mathematical Journal 53, 1546–1553 (2001). https://doi.org/10.1023/A:1014327010910

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  • DOI: https://doi.org/10.1023/A:1014327010910

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