一维 p 拉普拉斯电位节点的完全连续性和弗雷谢特导数

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2024-11-15 DOI:10.1016/j.jde.2024.11.008

Jifeng Chu , Gang Meng , Feng Wang , Meirong Zhang

{"title":"一维 p 拉普拉斯电位节点的完全连续性和弗雷谢特导数","authors":"Jifeng Chu , Gang Meng , Feng Wang , Meirong Zhang","doi":"10.1016/j.jde.2024.11.008","DOIUrl":null,"url":null,"abstract":"<div><div>The aim of this paper is to study the dependence of all nodes on integrable potentials, for one-dimensional <em>p</em>-Laplacian with separated boundary conditions, including the complete continuity of nodes in potentials with the weak topology, and the continuous Fréchet differentiability of nodes in potentials. We present the precise formula for the Fréchet derivatives of nodes in potentials. These results are natural but nontrivial generalizations of those for Sturm-Liouville operators, with quite different proofs due to the nonlinearity of the <em>p</em>-Laplacian.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"416 ","pages":"Pages 1960-1976"},"PeriodicalIF":2.4000,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Complete continuity and Fréchet derivatives of nodes in potentials for one-dimensional p-Laplacian\",\"authors\":\"Jifeng Chu , Gang Meng , Feng Wang , Meirong Zhang\",\"doi\":\"10.1016/j.jde.2024.11.008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The aim of this paper is to study the dependence of all nodes on integrable potentials, for one-dimensional <em>p</em>-Laplacian with separated boundary conditions, including the complete continuity of nodes in potentials with the weak topology, and the continuous Fréchet differentiability of nodes in potentials. We present the precise formula for the Fréchet derivatives of nodes in potentials. These results are natural but nontrivial generalizations of those for Sturm-Liouville operators, with quite different proofs due to the nonlinearity of the <em>p</em>-Laplacian.</div></div>\",\"PeriodicalId\":15623,\"journal\":{\"name\":\"Journal of Differential Equations\",\"volume\":\"416 \",\"pages\":\"Pages 1960-1976\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-11-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022039624007241\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039624007241","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文旨在研究具有分离边界条件的一维 p-Laplacian 的所有节点对可积分势的依赖性，包括具有弱拓扑的势中节点的完全连续性，以及势中节点的连续弗雷谢特可微分性。我们提出了势中节点弗雷谢特导数的精确公式。这些结果是对 Sturm-Liouville 算子结果的自然而非繁琐的概括，由于 p-Laplacian 的非线性，其证明方法大相径庭。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Complete continuity and Fréchet derivatives of nodes in potentials for one-dimensional p-Laplacian

The aim of this paper is to study the dependence of all nodes on integrable potentials, for one-dimensional p-Laplacian with separated boundary conditions, including the complete continuity of nodes in potentials with the weak topology, and the continuous Fréchet differentiability of nodes in potentials. We present the precise formula for the Fréchet derivatives of nodes in potentials. These results are natural but nontrivial generalizations of those for Sturm-Liouville operators, with quite different proofs due to the nonlinearity of the p-Laplacian.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics