A. Ardjouni and A. Djoudi PERIODIC SOLUTIONS IN TOTALLY NONLINEAR DYNAMIC EQUATIONS WITH FUNCTIONAL DELAY ON A TIME SCALE

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

Periodicity and Stability in Nonlinear Neutral Dynamic Equations with Infinite Delay on a Time Scale

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 contraction mapping principle. Also, by the...

Dynamic Systems and Applications 25 (2016) 253-262 STABILITY SOLUTIONS FOR A SYSTEM OF NONLINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH FUNCTIONAL DELAY

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.

Periodic Solutions for Third-order Nonlinear Delay Differential Equations with Variable Coefficients

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 existence and uniqueness of periodic solutions...

Existence of Periodic Solutions for a Second Order Nonlinear Neutral Differential Equation with Functional Delay

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 mappings, one is a large contraction an...