Geodesic
Periodic Solutions for Impulsive Neutral Dynamic Equations with Infinite Delay on Time Scales
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 1, p. 69 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $\mathbb{T}$ be a periodic time scale. We use the Krasnoselskii's fixed point theorem to show that the impulsive neutral dynamic equations with infinite delay \begin{align*} x^{\Delta}(t)=-A(t)x^{igma}(t)+g^{\Delta}(t,x(t-h(t)))+ıt_{-ıfty}^{t}Deft( t,u\right) f(x(u))riangle u, \quad teq t_{j}, tı\mathbb{T}, x(t_{j}^{+})=x(t_{j}^{-})+I_{j}(x(t_{j})),\quad jı\mathbb{Z}^{+}\end{align*} have a periodic solution. Under a slightly more stringent conditions we show that the periodic solution is unique using the contraction mapping principle.
Classification : 34N05, 34K13 34K40, 34K45
Keywords: Periodic solutions, neutral dynamic equations, impulses, Krasnoselskii fixed point, infinite delay, time scales 
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     author = {A. Ardjouni and A. Djoudi},
     title = {Periodic {Solutions} for {Impulsive} {Neutral} {Dynamic} {Equations} with {Infinite} {Delay} on {Time} {Scales}},
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A. Ardjouni; A. Djoudi. Periodic Solutions for Impulsive Neutral Dynamic Equations with Infinite Delay on Time Scales. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 1, p. 69 . http://geodesic.mathdoc.fr/item/KJM_2018_42_1_a5/