Abstract

The paper deals with a family of second-order partial differential equations on the complex plane. The coefficient of the unknown function depends on a natural parameter \(n\). Solutions of the equations are called generalized analytic functions of order \(n\). In a simply connected domain \(T^{+}\), we investigate Neumann boundary value problem for generalized analytic functions of order \(n\). If \(T^{+}\) is a disk, we suggest an explicit method for solving the problem in the class of first-order generalized analytic functions. We establish that the solvability of Neumann problem significantly depends on the value of radius of the disk.

中文翻译：

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圆盘中广义解析函数的诺依曼问题的可解性与其半径值的相关性

摘要

该论文涉及复平面上的一族二阶偏微分方程。未知函数的系数取决于自然参数\(n\)。方程的解称为\(n\)阶广义解析函数。在单连通域\(T^{+}\) 中，我们研究了\(n\)阶广义解析函数的 Neumann 边值问题。如果\(T^{+}\)是一个圆盘，我们建议在一阶广义解析函数类中使用显式方法来解决该问题。我们确定诺依曼问题的可解性很大程度上取决于圆盘的半径值。