Abstract

In previous papers, we obtained some delta-shaped partial solutions of odd-order equations with multiple characteristics and studied some of their properties. In this paper, we first obtain the necessary estimates at infinity for these solutions, and then construct a fundamental solution (FS) of an odd-order equation with multiple characteristics in a rectangular domain as the sum of these particular solutions. We show that the FS is a solution to an inhomogeneous equation with multiple characteristics in a rectangular domain. In turn, knowledge of FS allows us to construct a potential theory for its further use in solving boundary-value problems.

中文翻译：

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奇数次方程基本解的构造

摘要

在之前的论文中，我们获得了一些具有多重特征的奇数阶方程的δ型偏解，并研究了它们的一些性质。在本文中，我们首先获得这些解的无穷远必要估计，然后构造矩形域中具有多个特征的奇次方程的基本解（FS）作为这些特定解的总和。我们证明 FS 是矩形域中具有多个特征的非齐次方程的解。反过来，FS 的知识使我们能够构建一个潜在的理论，以进一步将其用于解决边值问题。