离散非线性基尔霍夫-乔夸德方程的解决方案

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-04 DOI:10.1007/s40840-024-01735-y

Lidan Wang

{"title":"离散非线性基尔霍夫-乔夸德方程的解决方案","authors":"Lidan Wang","doi":"10.1007/s40840-024-01735-y","DOIUrl":null,"url":null,"abstract":"In this paper, we study the discrete Kirchhoff–Choquard equation $$\\begin{aligned} -\\left( a+b \\int _{{\\mathbb {Z}}^3}|\\nabla u|^{2} d \\mu \\right) \\Delta u+V(x) u=\\left( R_{\\alpha } *F(u)\\right) f(u),\\quad x\\in {\\mathbb {Z}}^3, \\end{aligned}$$where \$a,\\,b>0\$, \$\\alpha \\in (0,3)\$ are constants and \$R_{\\alpha }\$ is the Green’s function of the discrete fractional Laplacian that behaves as the Riesz potential. Under some suitable assumptions on V and f, we prove the existence of nontrivial solutions and ground state solutions respectively by variational methods.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solutions to discrete nonlinear Kirchhoff–Choquard equations\",\"authors\":\"Lidan Wang\",\"doi\":\"10.1007/s40840-024-01735-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study the discrete Kirchhoff–Choquard equation $$\\\\begin{aligned} -\\\\left( a+b \\\\int _{{\\\\mathbb {Z}}^3}|\\\\nabla u|^{2} d \\\\mu \\\\right) \\\\Delta u+V(x) u=\\\\left( R_{\\\\alpha } *F(u)\\\\right) f(u),\\\\quad x\\\\in {\\\\mathbb {Z}}^3, \\\\end{aligned}$$where \\\$a,\\\\,b>0\\\$, \\\$\\\\alpha \\\\in (0,3)\\\$ are constants and \\\$R_{\\\\alpha }\\\$ is the Green’s function of the discrete fractional Laplacian that behaves as the Riesz potential. Under some suitable assumptions on V and f, we prove the existence of nontrivial solutions and ground state solutions respectively by variational methods.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2024-07-04\",\"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://doi.org/10.1007/s40840-024-01735-y\",\"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://doi.org/10.1007/s40840-024-01735-y","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，我们研究了离散基尔霍夫-乔夸德方程 $$begin{aligned} -\left( a+b \int _{\mathbb {Z}}^3}|\nabla u|^{2} d \mu \right) \Delta u+V(x) u=\left( R_{\alpha } *F(u) \right*F(u)\right) f(u),\quad x\in {\mathbb {Z}}^3, \end{aligned}$$其中$a,\,b>0$,$\alpha \in (0,3)$ 是常数，$R_{\alpha }$ 是离散分数拉普拉斯函数的格林函数，表现为里兹势。在关于 V 和 f 的一些适当假设下，我们通过变分法分别证明了非小解和基态解的存在性。

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

Solutions to discrete nonlinear Kirchhoff–Choquard equations

In this paper, we study the discrete Kirchhoff–Choquard equation

$$\begin{aligned} -\left( a+b \int _{{\mathbb {Z}}^3}|\nabla u|^{2} d \mu \right) \Delta u+V(x) u=\left( R_{\alpha } *F(u)\right) f(u),\quad x\in {\mathbb {Z}}^3, \end{aligned}$$

where $a,\,b>0$, $\alpha \in (0,3)$ are constants and $R_{\alpha }$ is the Green’s function of the discrete fractional Laplacian that behaves as the Riesz potential. Under some suitable assumptions on V and f, we prove the existence of nontrivial solutions and ground state solutions respectively by variational methods.

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.