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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Global convergence to equilibria in non-monotone delay differential equations


Authors: Hassan A. El-Morshedy and Alfonso Ruiz-Herrera
Journal: Proc. Amer. Math. Soc. 147 (2019), 2095-2105
MSC (2010): Primary 34K25, 92B99
DOI: https://doi.org/10.1090/proc/14360
Published electronically: January 28, 2019
MathSciNet review: 3937685
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Abstract: In this paper we derive some criteria of global attraction to a positive equilibrium for the equation

$\displaystyle x'(t)=-\beta x(t)+\beta F(x(t-\sigma ),x(t-\tau )),$    

where $ 0\leq \sigma \leq \tau $, $ \beta >0$, and $ F:[0,\infty )^{2}\longrightarrow [0,\infty )$ is a smooth map. The method of proof is reminiscent to the classical approach of ``decomposing +embedding''. Our results have two strengths: (i) We derive delay-dependent conditions of global attraction. (ii) We impose monotonicity conditions only on the second variable of $ F$.

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Additional Information

Hassan A. El-Morshedy
Affiliation: Departament of Mathematics, Faculty of Science, Damietta University, Egypt
Email: elmorshedy@yahoo.com

Alfonso Ruiz-Herrera
Affiliation: Departament of Mathematics, University of Oviedo, Spain
Email: ruizalfonso@uniovi.es

DOI: https://doi.org/10.1090/proc/14360
Received by editor(s): April 9, 2018
Received by editor(s) in revised form: August 7, 2018
Published electronically: January 28, 2019
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society