有界圆柱体中的半线性方程：莫尔斯指数和一维解的分岔

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-01 DOI:10.1016/j.jmaa.2024.128918

Danilo Gregorin Afonso

{"title":"有界圆柱体中的半线性方程：莫尔斯指数和一维解的分岔","authors":"Danilo Gregorin Afonso","doi":"10.1016/j.jmaa.2024.128918","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study semilinear elliptic equations in domains where there is a natural class of solutions, which depend only on one variable, and whose simple geometry reflects the geometry of the domain. We prove that under quite general assumptions, other types of solutions also exist. More precisely, we consider one-dimensional solutions in bounded cylinders and, combining a suitable separation of variables with the theory of ordinary differential equations, we show how to compute the Morse index of such solutions. The Morse index is then used to prove local and global bifurcation results.</div></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Semilinear equations in bounded cylinders: Morse index and bifurcation from one-dimensional solutions\",\"authors\":\"Danilo Gregorin Afonso\",\"doi\":\"10.1016/j.jmaa.2024.128918\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we study semilinear elliptic equations in domains where there is a natural class of solutions, which depend only on one variable, and whose simple geometry reflects the geometry of the domain. We prove that under quite general assumptions, other types of solutions also exist. More precisely, we consider one-dimensional solutions in bounded cylinders and, combining a suitable separation of variables with the theory of ordinary differential equations, we show how to compute the Morse index of such solutions. The Morse index is then used to prove local and global bifurcation results.</div></div>\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X24008400\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24008400","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们研究了域中的半线性椭圆方程，在这些域中存在一类自然解，它们只取决于一个变量，其简单的几何形状反映了域的几何形状。我们证明，在相当一般的假设条件下，也存在其他类型的解。更确切地说，我们考虑了有界圆柱体中的一维解，并结合适当的变量分离和常微分方程理论，说明了如何计算这类解的莫尔斯指数。然后利用莫尔斯指数证明局部和全局分岔结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Semilinear equations in bounded cylinders: Morse index and bifurcation from one-dimensional solutions

In this paper, we study semilinear elliptic equations in domains where there is a natural class of solutions, which depend only on one variable, and whose simple geometry reflects the geometry of the domain. We prove that under quite general assumptions, other types of solutions also exist. More precisely, we consider one-dimensional solutions in bounded cylinders and, combining a suitable separation of variables with the theory of ordinary differential equations, we show how to compute the Morse index of such solutions. The Morse index is then used to prove local and global bifurcation results.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.