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/