具有指数非线性和二维对流项的椭圆系统的一些存在性结果

IF 0.7 4区数学 Q2 MATHEMATICS

Topological Methods in Nonlinear Analysis Pub Date : 2022-12-10 DOI:10.12775/tmna.2022.025

W. Liu

{"title":"具有指数非线性和二维对流项的椭圆系统的一些存在性结果","authors":"W. Liu","doi":"10.12775/tmna.2022.025","DOIUrl":null,"url":null,"abstract":"In this paper, we establish the existence of solutions to a class of elliptic systems.\nThe nonlinearities include exponential growth terms and convection terms.\n The exponential growth term means it could be critical growth at $\\infty$.\nThe Trudinger-Moser inequality is used to deal with it. The convection term means\n it involves the gradient of unknown function.\nThe strong convergence of sequences is employed to overcome the difficulties caused by convection terms.\nThe variational methods are invalid and the Galerkin method and an approximation scheme are applied to obtain four different solutions.\nOur results supplements those from \\cite{Araujo2018}.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some existence results for elliptic systems with exponential nonlinearities and convection terms in dimension two\",\"authors\":\"W. Liu\",\"doi\":\"10.12775/tmna.2022.025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we establish the existence of solutions to a class of elliptic systems.\\nThe nonlinearities include exponential growth terms and convection terms.\\n The exponential growth term means it could be critical growth at $\\\\infty$.\\nThe Trudinger-Moser inequality is used to deal with it. The convection term means\\n it involves the gradient of unknown function.\\nThe strong convergence of sequences is employed to overcome the difficulties caused by convection terms.\\nThe variational methods are invalid and the Galerkin method and an approximation scheme are applied to obtain four different solutions.\\nOur results supplements those from \\\\cite{Araujo2018}.\",\"PeriodicalId\":23130,\"journal\":{\"name\":\"Topological Methods in Nonlinear Analysis\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-12-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topological Methods in Nonlinear Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.12775/tmna.2022.025\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topological Methods in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12775/tmna.2022.025","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文证明了一类椭圆系统解的存在性。非线性包括指数增长项和对流项。指数增长项意味着它可能是$\infty$的临界增长。使用Trudinger-Moser不等式来处理它。对流项意味着其涉及未知函数的梯度。利用序列的强收敛性来克服对流项带来的困难。变分方法是无效的，并且应用Galerkin方法和近似格式来获得四种不同的解。我们的结果补充了\cite{Araujo2018}的结果。

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

Some existence results for elliptic systems with exponential nonlinearities and convection terms in dimension two

In this paper, we establish the existence of solutions to a class of elliptic systems. The nonlinearities include exponential growth terms and convection terms. The exponential growth term means it could be critical growth at $\infty$. The Trudinger-Moser inequality is used to deal with it. The convection term means it involves the gradient of unknown function. The strong convergence of sequences is employed to overcome the difficulties caused by convection terms. The variational methods are invalid and the Galerkin method and an approximation scheme are applied to obtain four different solutions. Our results supplements those from \cite{Araujo2018}.

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

Topological Methods in Nonlinear Analysis 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.