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A multipoint problem for hyperbolic equations in the class of functions that are almost-periodic with respect to the spatial variables

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Abstract

We consider the analog of a multipoint problem on the time variable for a hyperbolic equation with constant coefficients and an arbitrary number of spatial variables. The solution of the problem is sought in the class of functions that are almost-periodic on the spatial variables, whose spectrum has a point of accumulation at infinity. The existence of a solution of the problem is connected with the problem of small denominators. The central point of the article is occupied by a theorem on a lower estimate of the small denominators that arise in constructing a solution of the problem.

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Literature cited

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Authors
  1. B. I. Ptashnik
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  2. P. I. Shatabalyuk
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Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 210–215.

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Ptashnik, B.I., Shatabalyuk, P.I. A multipoint problem for hyperbolic equations in the class of functions that are almost-periodic with respect to the spatial variables. J Math Sci 67, 3025–3030 (1993). https://doi.org/10.1007/BF01095890

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  • DOI: https://doi.org/10.1007/BF01095890

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