Mathematica Bohemica, first online, pp. 1-21


New sufficient conditions for global asymptotic stability of a kind of nonlinear neutral differential equations

Mimia Benhadri, Tomás Caraballo

Received May 6, 2020.   Published online September 9, 2021.

Abstract:  This paper addresses the stability study for nonlinear neutral differential equations. Thanks to a new technique based on the fixed point theory, we find some new sufficient conditions ensuring the global asymptotic stability of the solution. In this work we extend and improve some related results presented in recent works of literature. Two examples are exhibited to show the effectiveness and advantage of the results proved.
Keywords:  contraction mapping principle; asymptotic stability; neutral differential equation
Classification MSC:  34K20, 34K13, 92B20
DOI:  10.21136/MB.2021.0079-20

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Affiliations:   Mimia Benhadri, Faculty of Sciences, Department of Mathematics, University 20 August 1955, P.O. Box 26, Skikda 21000, Algeria, e-mail: mbenhadri@yahoo.com; Tomás Caraballo, Departamento de Ecuaciones Difererenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, c/ Tarfia s/n, 41012-Sevilla, Spain, e-mail: caraball@us.es


 
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