一种非线性四阶积分微分方程的单调迭代技术及其应用

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Advances in Mathematical Physics Pub Date : 2024-04-25 DOI:10.1155/2024/8847784

Yan Wang, Jinxiang Wang, Xiaobin Yao

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引用次数: 0

摘要

在本文中，我们考虑了一类具有纳维边界条件的非线性四阶积分微分方程（IDE）解的存在性和迭代逼近问题。我们首先证明了线性四阶积分微分方程解析解的存在性和唯一性，该方程在工程学和物理学中有着丰富的应用，然后我们建立了相应算子的最大值原理。根据最大值原理，我们开发了一种存在下解和上解的单调迭代技术，从而在一定条件下获得非局部非线性问题的迭代解。本文列举了一些例子来说明主要结果。

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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Monotone Iterative Technique for a Kind of Nonlinear Fourth-Order Integro-Differential Equations and Its Application

In this paper, we consider the existence and iterative approximation of solutions for a class of nonlinear fourth-order integro-differential equations (IDEs) with Navier boundary conditions. We first prove the existence and uniqueness of analytical solutions for a linear fourth-order IDE, which has rich applications in engineering and physics, and then we establish a maximum principle for the corresponding operator. Based upon the maximum principle, we develop a monotone iterative technique in the presence of lower and upper solutions to obtain iterative solutions for the nonlocal nonlinear problem under certain conditions. Some examples are presented to illustrate the main results.

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来源期刊

Advances in Mathematical Physics 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

151

审稿时长

>12 weeks

期刊介绍： Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.