Abdelouaheb Ardjouni

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In this article we study the existence of periodic solutions of the second order nonlinear neutral differential equation with functional delay d dt x (t) + p (t) d dt x (t) + q (t) x (t) = d dt g (t, x (t− τ (t))) + f ` t, x (t) , x (t− τ (t)) ́ . The main tool employed here is the Burton-Krasnoselskii’s hybrid fixed point theorem dealing with a sum of two(More)
In this article we study the existence of positive periodic solutions for two types of third-order nonlinear neutral differential equation with variable delay. The main tool employed here is the Krasnoselskii’s fixed point theorem dealing with a sum of two mappings, one is a contraction and the other is completely continuous. The results obtained here(More)
In this paper, we study the existence of positive periodic solutions of the nonlinear neutral di¤erential equation with variable delay d dt (x (t) g (t; x (t (t)))) = r (t)x (t) f (t; x (t (t))) : The main tool employed here is the Krasnoselskii’s hybrid …xed point theorem dealing with a sum of two mappings, one is a contraction and the other is compact.(More)
Abstract. The purpose of this paper is to use a fixed point approach 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. In our consideration we allow the coefficient functions to change sign and do not require bounded(More)
In this paper we use fixed point techniques to obtain asymptotic stability results of the zero solution of a nonlinear neutral differential equation with variable delays. This investigation uses new conditions which allow the coefficient functions to change sign and do not require the boundedness of delays. An asymptotic stability theorem with a necessary(More)
Let T be a periodic time scale. We use a fixed point theorem due to Krasnoselskii to show that the nonlinear neutral dynamic equation with infinite delay x(t) = −a(t)x(t) + (Q(t, x(t− g(t))))) + ∫ t −∞ D (t, u) f (x(u)) ∆u, t ∈ T, has a periodic solution. Under a slightly more stringent inequality we show that the periodic solution is unique using the(More)
Abstract. 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(More)
In this paper, we use the fixed point theorem to obtain stability results of the zero solution of a nonlinear neutral system of differential equations with functional delay. Application to the second-order model is given with an example. AMS (MOS) Subject Classification. 34K20, 34K40, 34A34, 35A08.
In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x′′′(t) + p(t)x′′(t) + q(t)x′(t) + r(t)x(t) = f (t, x (t) , x(t− τ(t))) + d dt g (t, x (t− τ (t))) , is considered. By employing Green’s function, Krasnoselskii’s fixed point theorem and the contraction mapping principle, we state and prove the(More)
We study the existence of periodic solutions of the second order nonlinear neutral differential equation with variable delay x′′ (t) + p (t)x′ (t) + q (t)h (x (t)) = c (t)x′ (t− τ (t)) + f (t, x (t− τ (t))) . We invert the given equation to obtain an integral, but equivalent, equation from which we define a fixed point mapping written as a sum of a large(More)