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

Adrian Nicolae Branga; Adrian Nicolae Branga

doi:10.3934/era.2022101

Electronic Research Archive

2022, Volume 30, Issue 6: 1999-2017. doi: 10.3934/era.2022101

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Research article

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

Adrian Nicolae Branga ^,

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

Received: 12 January 2022 Revised: 30 March 2022 Accepted: 01 April 2022 Published: 12 April 2022

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.
Citation: Adrian Nicolae Branga. Some conditions for the existence and uniqueness of monotonic and positive solutions for nonlinear systems of ordinary differential equations[J]. Electronic Research Archive, 2022, 30(6): 1999-2017. doi: 10.3934/era.2022101

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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.

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