Geodesic
Existence, Uniqueness and Stability of Periodic Solutions for Nonlinear Neutral Dynamic Equations
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 189 .

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The nonlinear neutral dynamic equation with periodic coefficients\begin{align*} eft[ u(t)-g(u(t-au(t)))\right] ^{\Delta} =(t)-a(t)u^{igma}(t)-a(t)g(u^{igma}(t-au(t)))-h(u(t),u(t-au(t))) \end{align*} is considered in this work. By using Krasnoselskii's fixed point theorem we obtain the existence of periodic and positive periodic solutions and by contraction mapping principle we obtain the uniqueness. Stability results of this equation are analyzed. The results obtained here extend the work of Mesmouli, Ardjouni and Djoudi \cite{m}.
Classification : 34K13, 34A34, 34K30, 34L30
Keywords: fixed point, periodic solutions, stability, dynamic equations, time scales 
@article{KJM_2020_44_2_a2,
     author = {F. Bouchelaghem and A. Ardjouni and A. Djoudi},
     title = {Existence, {Uniqueness} and {Stability} of {Periodic} {Solutions} for {Nonlinear} {Neutral} {Dynamic} {Equations}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {189 },
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2020_44_2_a2/}
}
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F. Bouchelaghem; A. Ardjouni; A. Djoudi. Existence, Uniqueness and Stability of Periodic Solutions for Nonlinear Neutral Dynamic Equations. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 189 . http://geodesic.mathdoc.fr/item/KJM_2020_44_2_a2/