一个带权离散椭圆型问题的变分方法

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization 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。

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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

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.