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}
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.
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
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