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In this paper we use the contraction mapping theorem to obtain asymptotic stability results of the zero solution of a nonlinear neutral Volterra integro-differential equation with variable delays. Some conditions which allow the coefficient functions to change sign and do not ask the boundedness of delays are given. An asymptotic stability theorem with a… (More)

In this article we study the existence of periodic solutions of the second order nonlinear neutral differential equation with functional delay d 2 dt 2 x (t) + p (t) d dt x (t) + q (t) x 3 (t) = d dt g (t, x (t − τ (t))) + f ` t, x 3 (t) , x 3 (t − τ (t)) ´. The main tool employed here is the Burton-Krasnoselskii's hybrid fixed point theorem dealing with a… (More)

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