On a Brezis-Oswald-type result for degenerate Kirchhoff problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/dcds.2023122

Stefano Biagi, Eugenio Vecchi

引用次数: 0

Abstract

In the present note we establish an almost-optimal solvability result for Kirchhoff-type problems of the following form$ \begin{cases} -M\big(\|\nabla u\|^2_{L^2(\Omega)}\big)\Delta u = f(x, u) & \text{in } \Omega , \\ u \geq 0, \, u\not\equiv 0 & \text{in } \Omega , \\ u = 0 & \text{on } \partial \Omega . \end{cases} $where $ f $ has sublinear growth and $ M $ is a non-decreasing map with $ M(0)\geq 0 $. Our approach is purely variational, and the result we obtain is resemblant to the one established by Brezis and Oswald (Nonlinear Anal., 1986) for sublinear elliptic equations.

查看原文本刊更多论文

简并Kirchhoff问题的brezis - oswald型结果

本文建立了以下形式$ \begin{cases} -M\big(\|\nabla u\|^2_{L^2(\Omega)}\big)\Delta u = f(x, u) & \text{in } \Omega , \\ u \geq 0, \, u\not\equiv 0 & \text{in } \Omega , \\ u = 0 & \text{on } \partial \Omega . \end{cases} $的kirchhoff型问题的几乎最优可解性结果，其中$ f $具有次线性增长，$ M $是与$ M(0)\geq 0 $的非递减映射。我们的方法是纯变分的，我们得到的结果类似于由Brezis和Oswald(非线性肛门)建立的结果。， 1986)求解次线性椭圆方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.