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Model Example for Study Smoothness of Solutions of Boundary-Value Problems for Differential-Difference Equations

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Abstract

The purpose of this article is to demonstrate with a simple example the complexities that arise when considering boundary-value problems for differential-difference equations. In this paper we discuss in detail smoothness issues of solutions to the Dirichlet problem for linear differential-difference equation with integer shifts. After analysis of this example we consider more general statement of the problem and certain results concerning the solvability and smoothness of solutions.

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Funding

This work is supported by the Ministry of Science and Higher Education of the Russian Federation: agreement no. 075-03-2020-223/3 (FSSF-2020-0018).

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), 117198, Moscow, Russia

    D. A. Neverova

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  1. D. A. Neverova
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Correspondence to D. A. Neverova.

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(Submitted by A. B. Muravnik)

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Neverova, D.A. Model Example for Study Smoothness of Solutions of Boundary-Value Problems for Differential-Difference Equations. Lobachevskii J Math 42, 967–973 (2021). https://doi.org/10.1134/S1995080221050115

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  • DOI: https://doi.org/10.1134/S1995080221050115

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