具有消失势和指数临界增长的平面Schrödinger-Poisson系统

Pub Date : 2023-09-23 DOI:10.12775/tmna.2022.058

Francisco S. B. Albuquerque, Jonison L. Carvalho, Marcelo F. Furtado, Everaldo S. Medeiros

{"title":"具有消失势和指数临界增长的平面Schrödinger-Poisson系统","authors":"Francisco S. B. Albuquerque, Jonison L. Carvalho, Marcelo F. Furtado, Everaldo S. Medeiros","doi":"10.12775/tmna.2022.058","DOIUrl":null,"url":null,"abstract":"In this paper we look for ground state solutions of the elliptic system $$ \\begin{cases} -\\Delta u+V(x)u+\\gamma\\phi K(x)u = Q(x)f(u), &x\\in\\mathbb{R}^{2}, \\\\ \\Delta \\phi =K(x) u^{2}, &x\\in\\mathbb{R}^{2}, \\end{cases} $$% where $\\gamma> 0$ and the continuous potentials $V$, $K$, $Q$ satisfy some mild growth conditions and the nonlinearity $f$ has exponential critical growth. The key point of our approach is a new version of the Trudinger-Moser inequality for weighted Sobolev space.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A planar Schrödinger-Poisson system with vanishing potentials and exponential critical growth\",\"authors\":\"Francisco S. B. Albuquerque, Jonison L. Carvalho, Marcelo F. Furtado, Everaldo S. Medeiros\",\"doi\":\"10.12775/tmna.2022.058\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we look for ground state solutions of the elliptic system $$ \\\\begin{cases} -\\\\Delta u+V(x)u+\\\\gamma\\\\phi K(x)u = Q(x)f(u), &x\\\\in\\\\mathbb{R}^{2}, \\\\\\\\ \\\\Delta \\\\phi =K(x) u^{2}, &x\\\\in\\\\mathbb{R}^{2}, \\\\end{cases} $$% where $\\\\gamma> 0$ and the continuous potentials $V$, $K$, $Q$ satisfy some mild growth conditions and the nonlinearity $f$ has exponential critical growth. The key point of our approach is a new version of the Trudinger-Moser inequality for weighted Sobolev space.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-09-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12775/tmna.2022.058\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12775/tmna.2022.058","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

本文寻找椭圆系统的基态解 $$ \begin{cases} -\Delta u+V(x)u+\gamma\phi K(x)u = Q(x)f(u), &x\in\mathbb{R}^{2}, \\ \Delta \phi =K(x) u^{2}, &x\in\mathbb{R}^{2}, \end{cases} $$% where $\gamma> 0$ and the continuous potentials $V$, $K$, $Q$ satisfy some mild growth conditions and the nonlinearity $f$ has exponential critical growth. The key point of our approach is a new version of the Trudinger-Moser inequality for weighted Sobolev space.

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

A planar Schrödinger-Poisson system with vanishing potentials and exponential critical growth

In this paper we look for ground state solutions of the elliptic system $$ \begin{cases} -\Delta u+V(x)u+\gamma\phi K(x)u = Q(x)f(u), &x\in\mathbb{R}^{2}, \\ \Delta \phi =K(x) u^{2}, &x\in\mathbb{R}^{2}, \end{cases} $$% where $\gamma> 0$ and the continuous potentials $V$, $K$, $Q$ satisfy some mild growth conditions and the nonlinearity $f$ has exponential critical growth. The key point of our approach is a new version of the Trudinger-Moser inequality for weighted Sobolev space.

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