具有不定非线性和缺乏紧性的非局部Kirchhoff超线性方程

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2016-09-29 DOI:10.1515/ijnsns-2016-0006

Lin Li, V. Rǎdulescu, Dušan D. Repovš

{"title":"具有不定非线性和缺乏紧性的非局部Kirchhoff超线性方程","authors":"Lin Li, V. Rǎdulescu, Dušan D. Repovš","doi":"10.1515/ijnsns-2016-0006","DOIUrl":null,"url":null,"abstract":"Abstract We study the following Kirchhoff equation: (K) −1+b∫ℝ3|∇u|2dxΔu+V(x)u=f(x,u),x∈ℝ3.$$ - \\left({1 + b\\int_{{{\\mathbb R}^3}} |\\nabla u{|^2}dx} \\right)\\Delta u + V(x)u = f(x, u), \\quad x \\in {{\\mathbb R}^3}. $$ A feature of this paper is that the nonlinearity f$f$ and the potential V$V$ are indefinite, hence sign-changing. Under some appropriate assumptions on V$V$ and f$f$ , we prove the existence of two different solutions of the equation via the Ekeland variational principle and the mountain pass theorem.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2016-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/ijnsns-2016-0006","citationCount":"7","resultStr":"{\"title\":\"Nonlocal Kirchhoff Superlinear Equations with Indefinite Nonlinearity and Lack of Compactness\",\"authors\":\"Lin Li, V. Rǎdulescu, Dušan D. Repovš\",\"doi\":\"10.1515/ijnsns-2016-0006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We study the following Kirchhoff equation: (K) −1+b∫ℝ3|∇u|2dxΔu+V(x)u=f(x,u),x∈ℝ3.$$ - \\\\left({1 + b\\\\int_{{{\\\\mathbb R}^3}} |\\\\nabla u{|^2}dx} \\\\right)\\\\Delta u + V(x)u = f(x, u), \\\\quad x \\\\in {{\\\\mathbb R}^3}. $$ A feature of this paper is that the nonlinearity f$f$ and the potential V$V$ are indefinite, hence sign-changing. Under some appropriate assumptions on V$V$ and f$f$ , we prove the existence of two different solutions of the equation via the Ekeland variational principle and the mountain pass theorem.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2016-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/ijnsns-2016-0006\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1515/ijnsns-2016-0006\",\"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":"5","ListUrlMain":"https://doi.org/10.1515/ijnsns-2016-0006","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: 7

摘要

摘要研究了下述Kirchhoff方程:(K)−1+b∫∈3|∇u|2dxΔu+V(x)u=f(x,u)，x∈∈∈3。$$ - \left({1 + b\int_{{{\mathbb R}^3}} |\nabla u{|^2}dx} \right)\Delta u + V(x)u = f(x, u), \quad x \in {{\mathbb R}^3}. $$本文的一个特点是非线性f $f$和势V $V$是不确定的，因此是变符号的。在V $V$和f $f$的适当假设下，利用Ekeland变分原理和山口定理证明了方程两种不同解的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Nonlocal Kirchhoff Superlinear Equations with Indefinite Nonlinearity and Lack of Compactness

Abstract We study the following Kirchhoff equation: (K) −1+b∫ℝ3|∇u|2dxΔu+V(x)u=f(x,u),x∈ℝ3.$$ - \left({1 + b\int_{{{\mathbb R}^3}} |\nabla u{|^2}dx} \right)\Delta u + V(x)u = f(x, u), \quad x \in {{\mathbb R}^3}. $$ A feature of this paper is that the nonlinearity f$f$ and the potential V$V$ are indefinite, hence sign-changing. Under some appropriate assumptions on V$V$ and f$f$ , we prove the existence of two different solutions of the equation via the Ekeland variational principle and the mountain pass theorem.

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.