Georgian Mathematical Journal 13 (2006), No. 1, 025--034
Copyright Heldermann Verlag 2006
Fixed Point Techniques and Stability for Neutral Nonlinear Differential Equations with Unbounded Delays
Ahcene Djoudi
Institut de Mathématiques, Faculté des Sciences, Université Badji Mokhtar, P.O. Box 12, 23000 Annaba, Algeria
adjoudi@yahoo.com
Rabah Khemis
Institut de Mathématiques, Faculté des Sciences, Université Badji Mokhtar, P.O. Box 12, 23000 Annaba, Algeria
[Abstract-pdf]
We use the contraction mapping theorem to obtain stability results of the scalar nonlinear neutral differential equation with functional delay $$ x^{\prime }(t)=-ax(t)+b(t)x^{2}(t-r(t))+c(t)x(t-r(t))x^{\prime }(t-r(t)). $$
Keywords: Contraction mapping, stability, nonlinear neutral differential equation, integral equation.
MSC: 34K20, 47H10
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