On the localization and numerical computation of positive radial solutions for ϕ -Laplace equations in the annulus

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.14232/ejqtde.2022.1.47

Equations Jorge Rodríguez–López, R. Precup, C. Gheorghiu

引用次数: 0

Abstract

The paper deals with the existence and localization of positive radial solutions for stationary partial differential equations involving a general ϕ -Laplace operator in the annulus. Three sets of boundary conditions are considered: Dirichlet–Neumann, Neumann–Dirichlet and Dirichlet–Dirichlet. The results are based on the homotopy version of Krasnosel'skii's fixed point theorem and Harnack type inequalities, first established for each one of the boundary conditions. As a consequence, the problem of multiple solutions is solved in a natural way. Numerical experiments confirming the theory, one for each of the three sets of boundary conditions, are performed by using the MATLAB object-oriented package Chebfun.

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环空中φ -Laplace方程径向正解的局部化与数值计算

本文讨论了环空中含有广义φ -拉普拉斯算子的平稳偏微分方程正径向解的存在性和局域性。考虑了三组边界条件:Dirichlet-Neumann、Neumann-Dirichlet和Dirichlet-Dirichlet。结果是基于Krasnosel'skii's不动点定理的同伦版本和Harnack型不等式，首先为每个边界条件建立。因此，多重解决方案的问题以一种自然的方式得到了解决。利用MATLAB面向对象软件包Chebfun对三组边界条件分别进行了数值实验，验证了这一理论。

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.