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Classical Solutions of Hyperbolic Differential-Difference Equations with Several Nonlocal Terms

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Abstract

A one-parameter family of smooth solutions of a two-dimensional differential-difference hyperbolic equation with \(n\) translations with respect to the spatial variable is constructed. The theorem is proved that the obtained solutions are classical if the real part of the symbol of the difference operator of the equation is positive. The class of equations such that the specified condition is satisfied for them and only for them is selected.

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ACKNOWLEDGMENTS

The author expresses her profound gratitude to A.B. Muravnik for his guidance.

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Authors and Affiliations

  1. Moscow State University, 119991, Moscow, Russia

    N. V. Zaitseva

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  1. N. V. Zaitseva
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Correspondence to N. V. Zaitseva.

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(Submitted by A. B. Muravnik)

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Zaitseva, N.V. Classical Solutions of Hyperbolic Differential-Difference Equations with Several Nonlocal Terms. Lobachevskii J Math 42, 231–236 (2021). https://doi.org/10.1134/S1995080221010285

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  • DOI: https://doi.org/10.1134/S1995080221010285

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