Stability in totally nonlinear neutral differential equations with variable delay using fixed point theory

The totally nonlinear neutral differential equation (d/ dt) (x(t))=−a(t)g(x(t−τ (t))) + (d/ dt)( G(t,x(t−τ (t)))), with variable delay &#964(t) &#8805 0 is investigated. We find suitable conditions for t, a, g and G so that for a given continuous...

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Autores principales:	Ardjouni,Abdelouaheb, Djoudi,Ahcene
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2015
Materias:	Fixed points Stability Neutral differential equations Variable delays
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000100003
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spelling	oai:scielo:S0716-091720150001000032015-07-13Stability in totally nonlinear neutral differential equations with variable delay using fixed point theoryArdjouni,AbdelouahebDjoudi,Ahcene Fixed points Stability Neutral differential equations Variable delays The totally nonlinear neutral differential equation (d/ dt) (x(t))=−a(t)g(x(t−τ (t))) + (d/ dt)( G(t,x(t−τ (t)))), with variable delay &#964(t) &#8805 0 is investigated. We find suitable conditions for t, a, g and G so that for a given continuous initial function 0 a mapping P for the above equation can be defined on a carefully chosen complete metric space S0&#968 ; and in which P possesses a unique fixed point. The final result is an asymptotic stability theorem for the zero solution with a necessary and sufficient condition. The obtained theorem improves and generalizes previous results due to Becker and Burton [6]. An example is given to illustrate our main result.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.34 n.1 20152015-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000100003en10.4067/S0716-09172015000100003
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Fixed points Stability Neutral differential equations Variable delays
spellingShingle	Fixed points Stability Neutral differential equations Variable delays Ardjouni,Abdelouaheb Djoudi,Ahcene Stability in totally nonlinear neutral differential equations with variable delay using fixed point theory
description	The totally nonlinear neutral differential equation (d/ dt) (x(t))=−a(t)g(x(t−τ (t))) + (d/ dt)( G(t,x(t−τ (t)))), with variable delay &#964(t) &#8805 0 is investigated. We find suitable conditions for t, a, g and G so that for a given continuous initial function 0 a mapping P for the above equation can be defined on a carefully chosen complete metric space S0&#968 ; and in which P possesses a unique fixed point. The final result is an asymptotic stability theorem for the zero solution with a necessary and sufficient condition. The obtained theorem improves and generalizes previous results due to Becker and Burton [6]. An example is given to illustrate our main result.
author	Ardjouni,Abdelouaheb Djoudi,Ahcene
author_facet	Ardjouni,Abdelouaheb Djoudi,Ahcene
author_sort	Ardjouni,Abdelouaheb
title	Stability in totally nonlinear neutral differential equations with variable delay using fixed point theory
title_short	Stability in totally nonlinear neutral differential equations with variable delay using fixed point theory
title_full	Stability in totally nonlinear neutral differential equations with variable delay using fixed point theory
title_fullStr	Stability in totally nonlinear neutral differential equations with variable delay using fixed point theory
title_full_unstemmed	Stability in totally nonlinear neutral differential equations with variable delay using fixed point theory
title_sort	stability in totally nonlinear neutral differential equations with variable delay using fixed point theory
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2015
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000100003
work_keys_str_mv	AT ardjouniabdelouaheb stabilityintotallynonlinearneutraldifferentialequationswithvariabledelayusingfixedpointtheory AT djoudiahcene stabilityintotallynonlinearneutraldifferentialequationswithvariabledelayusingfixedpointtheory
_version_	1718439802892713984

Stability in totally nonlinear neutral differential equations with variable delay using fixed point theory

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