Abstract

The Dirichlet problem for an elliptic functional differential equation involving a shifted and contracted argument under the Laplacian sign is studied. Sufficient conditions for the unique solvability of the problem are established. It is shown that the problem may have an infinite-dimensional solution manifold.

中文翻译：

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具有仿射变换的椭圆型泛函微分方程的Dirichlet问题。

摘要

研究了在拉普拉斯符号下具有变元和压缩变元的椭圆型泛函微分方程的Dirichlet问题。建立了解决该问题的独特条件的充分条件。结果表明，问题可能具有无穷大的解集。