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 τ(t) ≥ 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 S0ψ ; 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.
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Universidad Católica del Norte, Departamento de Matemáticas
2015
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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 τ(t) ≥ 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 S0ψ ; 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 |
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Ardjouni,Abdelouaheb Djoudi,Ahcene |
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Ardjouni,Abdelouaheb Djoudi,Ahcene Stability in totally nonlinear neutral differential equations with variable delay using fixed point theory |
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Ardjouni,Abdelouaheb Djoudi,Ahcene |
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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 |
| 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 τ(t) ≥ 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 S0ψ ; 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. |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2015 |
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http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172015000100003 |
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AT ardjouniabdelouaheb stabilityintotallynonlinearneutraldifferentialequationswithvariabledelayusingfixedpointtheory AT djoudiahcene stabilityintotallynonlinearneutraldifferentialequationswithvariabledelayusingfixedpointtheory |
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1755990051256270848 |