Multiplicity for a strongly singular quasilinear problem via bifurcation theory

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2021-03-13 DOI:10.1142/s1664360722500138

J. Giacomoni, Lais Moreira dos Santos, C. Santos

引用次数: 0

Abstract

A $p$-Laplacian elliptic problem in the presence of both strongly singular and $(p-1)$-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques and sub-supersolution method to establish the existence of an unbounded branch of positive solutions, which is bounded in positive $\lambda-$direction and bifurcates from infinity at $\lambda=0$. As consequence of the bifurcation result, we determine intervals of existence, nonexistence and, in particular cases, global multiplicity.

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用分岔理论研究一类强奇异拟线性问题的多重性

研究了一类具有强奇异和$(p-1)$-超线性非线性的$p$-拉普拉斯椭圆问题。利用分岔理论、近似技术和次超解方法，建立了正解的无界分支的存在性，该分支在正$\ λ -$方向上有界，并在$\ λ =0$处从无穷远分叉。作为分叉结果的结果，我们确定了存在和不存在的区间，并在特殊情况下确定了全局多重性的区间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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