一个带权离散椭圆型问题的变分方法

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2023-05-13 DOI:10.1080/01630563.2023.2208868

Maisam Boroun, S. Heidarkhani

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引用次数: 0

摘要

在本文中，我们关注由拉普拉斯驱动的离散边值问题的至少一个、两个和三个不同解的存在性。主要结果的证明依赖于变分方法。利用Bonanno的局部极小定理的一个结果，研究了带权问题的至少一个解和两个解的存在性。进一步利用两个临界点定理，一个是由于Averna和Bonanno，另一个是由于Bonanno，我们探讨了问题的两个解和三个解的存在性。为了说明主要结果，我们还提供了两个示例。

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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Variational Approaches to a Discrete Elliptic Problem with a Weight

Abstract In this article, we are concerned with the existence of at least one, two and three distinct solutions for discrete boundary value problems driven by the Laplacian. The proof of the main result depends on variational methods. By using a consequence of the local minimum theorem due Bonanno we investigate the existence of at least one solution and two solutions for the problem with the weight. Furthermore, by using two critical point theorems, one due Averna and Bonanno, and another due Bonanno we explore the existence of two and three solutions for the problem. We also provide two examples in order to illustrate the main results.

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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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