On stability functional differential equation with delay variable by using fixed point-theory

Abstract I will explain how to use the Banach fixed point theory in the asymptotic stability of nonlinear differential equations; I will obtain appropriate generalizations and strong forms of some of the results in [2, 3, 5, 6, 10, 11, 12,13]. Specifically, in the above-mentioned paper, asymptotic s...

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Autor principal:	Mohammed,Sizar Abid
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	Nonlinear Asymptotical stability Banach fixed point theorem Delayed functional differential equation
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200401
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spelling	oai:scielo:S0716-091720200002004012020-05-06On stability functional differential equation with delay variable by using fixed point-theoryMohammed,Sizar Abid Nonlinear Asymptotical stability Banach fixed point theorem Delayed functional differential equation Abstract I will explain how to use the Banach fixed point theory in the asymptotic stability of nonlinear differential equations; I will obtain appropriate generalizations and strong forms of some of the results in [2, 3, 5, 6, 10, 11, 12,13]. Specifically, in the above-mentioned paper, asymptotic stability is achieved, while I will discuss how to achieve a asymptotic stability as well as stability by making a simple observation, also circulate the previous asymptotic stability results to the Functional Differential Equations systems, not only on the scalar Functional Differential Equations as is the case in the mentioned paper. This raises the question of how much this particular method can afford us, and what are the limitations of this technique. I will refer to the important limitation of the fixed point theory on the uniqueness of solutions only within the complete metric space area where they are not specified. If the metric space onto which the contraction mapping principle is applied is very small, i do not get a satisfactory result. I will discuss this in detail below.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.2 20202020-04-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200401en10.22199/issn.0717-6279-2020-02-0024
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Nonlinear Asymptotical stability Banach fixed point theorem Delayed functional differential equation
spellingShingle	Nonlinear Asymptotical stability Banach fixed point theorem Delayed functional differential equation Mohammed,Sizar Abid On stability functional differential equation with delay variable by using fixed point-theory
description	Abstract I will explain how to use the Banach fixed point theory in the asymptotic stability of nonlinear differential equations; I will obtain appropriate generalizations and strong forms of some of the results in [2, 3, 5, 6, 10, 11, 12,13]. Specifically, in the above-mentioned paper, asymptotic stability is achieved, while I will discuss how to achieve a asymptotic stability as well as stability by making a simple observation, also circulate the previous asymptotic stability results to the Functional Differential Equations systems, not only on the scalar Functional Differential Equations as is the case in the mentioned paper. This raises the question of how much this particular method can afford us, and what are the limitations of this technique. I will refer to the important limitation of the fixed point theory on the uniqueness of solutions only within the complete metric space area where they are not specified. If the metric space onto which the contraction mapping principle is applied is very small, i do not get a satisfactory result. I will discuss this in detail below.
author	Mohammed,Sizar Abid
author_facet	Mohammed,Sizar Abid
author_sort	Mohammed,Sizar Abid
title	On stability functional differential equation with delay variable by using fixed point-theory
title_short	On stability functional differential equation with delay variable by using fixed point-theory
title_full	On stability functional differential equation with delay variable by using fixed point-theory
title_fullStr	On stability functional differential equation with delay variable by using fixed point-theory
title_full_unstemmed	On stability functional differential equation with delay variable by using fixed point-theory
title_sort	on stability functional differential equation with delay variable by using fixed point-theory
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000200401
work_keys_str_mv	AT mohammedsizarabid onstabilityfunctionaldifferentialequationwithdelayvariablebyusingfixedpointtheory
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On stability functional differential equation with delay variable by using fixed point-theory

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