洛伦兹-闵科夫斯基空间中涉及平均曲率算子的非线性方程存在多个径向解

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-17 DOI:arxiv-2409.11039

Vittorio Coti Zelati, Xu Dong, Yuanhong Wei

{"title":"洛伦兹-闵科夫斯基空间中涉及平均曲率算子的非线性方程存在多个径向解","authors":"Vittorio Coti Zelati, Xu Dong, Yuanhong Wei","doi":"arxiv-2409.11039","DOIUrl":null,"url":null,"abstract":"We prove existence of multiple radial solutions to the Dirichlet problem for\nnonlinear equations involving the mean curvature operator in Lorentz-Minkowski\nspace and a nonlinear term of concave-convex type. Solutions are found using\nSzulkin's critical point theory for non-smooth functional. Multiplicity results\nare also given for some cases in which the nonlinearity depends also on the\ngradient of the solution.","PeriodicalId":501165,"journal":{"name":"arXiv - MATH - Analysis of PDEs","volume":"19 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence of multiple radial solutions for nonlinear equation involving the mean curvature operator in Lorentz-Minkowski space\",\"authors\":\"Vittorio Coti Zelati, Xu Dong, Yuanhong Wei\",\"doi\":\"arxiv-2409.11039\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove existence of multiple radial solutions to the Dirichlet problem for\\nnonlinear equations involving the mean curvature operator in Lorentz-Minkowski\\nspace and a nonlinear term of concave-convex type. Solutions are found using\\nSzulkin's critical point theory for non-smooth functional. Multiplicity results\\nare also given for some cases in which the nonlinearity depends also on the\\ngradient of the solution.\",\"PeriodicalId\":501165,\"journal\":{\"name\":\"arXiv - MATH - Analysis of PDEs\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Analysis of PDEs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11039\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Analysis of PDEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11039","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了涉及洛伦兹-闵科夫斯基空间中平均曲率算子和凹凸型非线性项的非线性方程的 Dirichlet 问题存在多个径向解。利用非光滑函数的苏尔金临界点理论找到了解决方案。对于非线性也取决于解的梯度的某些情况，还给出了多重性结果。

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

Existence of multiple radial solutions for nonlinear equation involving the mean curvature operator in Lorentz-Minkowski space

We prove existence of multiple radial solutions to the Dirichlet problem for nonlinear equations involving the mean curvature operator in Lorentz-Minkowski space and a nonlinear term of concave-convex type. Solutions are found using Szulkin's critical point theory for non-smooth functional. Multiplicity results are also given for some cases in which the nonlinearity depends also on the gradient of the solution.

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

arXiv - MATH - Analysis of PDEs

自引率

0.00%

发文量