一维变权$ p $-拉普拉斯问题正解的存在性和多重性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/era.2023156

Liangying Miao, Man Xu, Zhiqian He

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引用次数: 0

摘要

本文证明了一维变权$ p $ -拉普拉斯问题的正解集包含一个反向的$ S $形连续体。根据非线性项在0和$ \infty $处的渐近性质，通过确定正解的无界连续体的形状，确定了$ p $ - laplace问题有一个或两个或三个正解的分岔参数区间。主要结果的证明是基于分岔技术的。

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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Existence and multiplicity of positive solutions for one-dimensional $ p $-Laplacian problem with sign-changing weight

In this paper, we show the positive solutions set for one-dimensional $ p $-Laplacian problem with sign-changing weight contains a reversed $ S $-shaped continuum. By figuring the shape of unbounded continuum of positive solutions, we identify the interval of bifurcation parameter in which the $ p $-Laplacian problem has one or two or three positive solutions according to the asymptotic behavior of nonlinear term at 0 and $ \infty $. The proof of the main result is based upon bifurcation technique.

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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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