Stability in Nonlinear Neutral Differential Equations with Infinite Delay
Mathematica Moravica, Tome 18 (2014) no. 2.

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In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the nonlinear neutral differential equation with infinite delay $\frac{\mathrm{d}}{\mathrm{d}t}x(t) = -a(t) x(t-\tau_{1}(t)) + \frac{\mathrm{d}}{\mathrm{d}t} Q(t, x(t-\tau_{2}(t))) + \int_{-\infty}^{t} D(t,s) f(x(s))\mathrm{d}s$. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some results due to Burton [6], Zhang [17], Althubiti, Makhzoum, Raffoul [1].
Mots-clés : Fixed points, Stability, Neutral differential equation, Integral equation, Infinite delay 
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Abdelouaheb Ardjouni; Ahcene Djoudi. Stability in Nonlinear Neutral Differential Equations with Infinite Delay. Mathematica Moravica, Tome 18 (2014) no. 2. https://geodesic-test.mathdoc.fr/item/MM3_2014_18_2_a7/