Hybrid localization for nonlinear systems: lower/upper solution and Krasnosel’skii fixed point theorem techniques

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URI: https://hdl.handle.net/10347/37659
E-ISSN: 1436-5081
DOI: 10.1007/s00605-024-02026-1

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2024

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Springer
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Abstract

We present a novel localization of the solutions of a system of two differential equations. It combines, in a component-wise manner, the method of lower and upper solutions with the localization provided by compression–expansion type fixed point theorems in cones. The main result is based on a recent fixed point theorem for operator systems.

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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00605-024-02026-1

Keywords

Nonlinear systems| Component-wise location| Lower and upper solution| Krasnosel’skiĭ fixed point theorem| Schauder fixed point theorem

Bibliographic citation

Rodríguez–López, J. Hybrid localization for nonlinear systems: lower/upper solution and Krasnosel’skiĭ fixed point theorem techniques. Monatsh Math (2024). https://doi.org/10.1007/s00605-024-02026-1

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Research partially supported by Ministerio de Ciencia y Tecnología (Spain), AEI and Feder, grant PID2020-113275GB-I00, and Xunta de Galicia, Spain, Project ED431C 2023/12.

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Estatística, Análise Matemática e Optimización
Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)