A hybrid Krasnosel’skiĭ-Schauder fixed point theorem for systems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-24 DOI:10.1016/j.nonrwa.2024.104165

Gennaro Infante , Giovanni Mascali , Jorge Rodríguez–López

引用次数: 0

Abstract

We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel’skiĭ cone compression–expansion type methodologies and Schauder-type ones. In particular we establish a localization of the solution of the system within the product of a conical shell and of a closed convex set. By iterating this procedure we prove the existence of multiple solutions. We illustrate our theoretical results by applying them to the solvability of systems of Hammerstein integral equations. In the case of two specific boundary value problems and with given nonlinearities, we are also able to obtain a numerical solution, consistent with our theoretical results.

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系统的克拉斯诺瑟尔斯基-肖德尔混合定点定理

我们提供了有关非线性算子系统解定位的新结果。我们结合使用了 Krasnosel'skiĭ 圆锥压缩-展开类型方法和 Schauder 类型方法。特别是，我们在圆锥壳和封闭凸集的乘积内建立了系统解的定位。通过迭代这一过程，我们证明了多重解的存在。我们将理论结果应用于哈默斯坦积分方程系统的可解性，以说明我们的理论结果。在两个特定边界值问题和给定非线性的情况下，我们也能获得与理论结果一致的数值解。

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.