上半平面非线性高阶方程的 Dirichlet 问题

Pub Date : 2024-06-25 DOI:10.1007/s11785-024-01566-6

Pelin Ayşe Gökgöz

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引用次数: 0

摘要

本文考虑了上半平面非线性高阶方程的 Dirichlet 问题。首先，我们介绍了上半平面非均质多解析方程的解。然后，我们研究相关积分算子的性质。最后，我们将上半平面非线性高阶方程的 Dirichlet 问题转化为积分微分方程系，并利用巴拿赫定点定理得到唯一解的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Dirichlet Problem for Nonlinear Higher-Order Equations in Upper Half Plane

In this article, we consider the Dirichlet problem for nonlinear higher-order equations in upper half plane. Firstly we introduce the solutions of inhomogeneous polyanalytic equation in upper half plane. Then we investigate the properties of relevant integral operators. Lastly we transform the Dirichlet problem for nonlinear higher-order equations in upper half plane into the system of integro-differential equations and we obtain the existence of unique solution using Banach fixed point theorem.

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