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Fixed points and stability in nonlinear neutral differential equations with variable delays

Abdelouaheb Ardjouni, Ahcene Djoudi


In this paper we use the contraction mapping theorem to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved, which improves and generalizes some previous results due to T. A. Burton [6], B. Zhang [20], Y. M. Dib, M. R. Maroun, Y. N. Raffoul [14]. Two examples are also given to illustrate our work.

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