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.

中文翻译：

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研究微分方程边值问题解的平滑性的模型实例

摘要

本文的目的是通过一个简单的例子来说明在考虑微分差分方程的边值问题时出现的复杂性。在本文中，我们详细讨论了整数位移线性微分差分方程狄利克雷问题解的平滑性问题。在分析了这个例子之后，我们考虑了对问题的更一般性的陈述以及关于解的可解性和平滑性的某些结果。