具有消失势的扰动 $$1-$Laplacian 和 $$1-$ 双谐波问题的有界变化解的存在性结果

IF 0.8 Q2 MATHEMATICS Advances in Operator Theory Pub Date : 2024-06-06 DOI:10.1007/s43036-024-00351-8

Mahsa Amoie, Mohsen Alimohammady

{"title":"具有消失势的扰动 $$1-$Laplacian 和 $$1-$ 双谐波问题的有界变化解的存在性结果","authors":"Mahsa Amoie, Mohsen Alimohammady","doi":"10.1007/s43036-024-00351-8","DOIUrl":null,"url":null,"abstract":"<div><p>This work focuses on the investigation of a quasilinear elliptic problem in the entire space <span>\$\\mathbb {R}^N\$</span>, which involves the 1-Laplacian and 1-biharmonic operators, as well as potentials that can vanish at infinity. This research is conducted within the space of functions with bounded variation. The main result is proven using a version of the mountain pass theorem that does not require the Palais-Smale condition.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 3","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence result of bounded variation solution for a perturbed \\\$1-\\\$Laplacian and \\\$1-\\\$biharmonic problem with vanishing potentials\",\"authors\":\"Mahsa Amoie, Mohsen Alimohammady\",\"doi\":\"10.1007/s43036-024-00351-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This work focuses on the investigation of a quasilinear elliptic problem in the entire space <span>\\\$\\\\mathbb {R}^N\\\$</span>, which involves the 1-Laplacian and 1-biharmonic operators, as well as potentials that can vanish at infinity. This research is conducted within the space of functions with bounded variation. The main result is proven using a version of the mountain pass theorem that does not require the Palais-Smale condition.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"9 3\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-06-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-024-00351-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00351-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

这项工作的重点是研究整个空间 $\mathbb {R}^N$ 中的准线性椭圆问题，该问题涉及 1 拉普拉斯算子和 1 双谐波算子，以及可以在无穷远处消失的势。这项研究是在有界变函数空间内进行的。主要结果是利用不需要 Palais-Smale 条件的山口定理版本证明的。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Existence result of bounded variation solution for a perturbed $1-$Laplacian and $1-$biharmonic problem with vanishing potentials

This work focuses on the investigation of a quasilinear elliptic problem in the entire space $\mathbb {R}^N$, which involves the 1-Laplacian and 1-biharmonic operators, as well as potentials that can vanish at infinity. This research is conducted within the space of functions with bounded variation. The main result is proven using a version of the mountain pass theorem that does not require the Palais-Smale condition.

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

Advances in Operator Theory MATHEMATICS-

CiteScore

1.60

自引率

0.00%

发文量