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Research Article | Open Access

Some conditions for the existence and uniqueness of monotonic and positive solutions for nonlinear systems of ordinary differential equations

Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, 5–7 Dr. I. Raţiu, Sibiu 550012, Romania
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Abstract

In this paper, applying the theory of fixed points in complete gauge spaces, we establish some conditions for the existence and uniqueness of monotonic and positive solutions for nonlinear systems of ordinary differential equations. Moreover, the paper contains an application of the theoretical results to the study of a class of systems of nonlinear ordinary differential equations.

Keywords

nonlinear systems of ordinary differential equationsmonotonic and positive solutionscomplete gauge spacesfixed point theoryexistence and uniqueness theorems

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Electronic Research Archive
Volume 30 Issue 6,
June 2022
Pages 1999-2017
DOI: 10.3934/era.2022101

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Cite this article:
Branga AN. Some conditions for the existence and uniqueness of monotonic and positive solutions for nonlinear systems of ordinary differential equations. Electronic Research Archive, 2022, 30(6): 1999-2017. https://doi.org/10.3934/era.2022101

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Received: 12 January 2022
Revised: 30 March 2022
Accepted: 01 April 2022
Published: 15 June 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)