Existence, Uniqueness and Stability of Periodic Solutions for Nonlinear Neutral Dynamic Equations

F. Bouchelaghem, A. Ardjouni, A. Djoudi

The nonlinear neutral dynamic equation with periodic coefficients\begin{align*} & eft[ u(t)-g(u(t-au(t)))\right] ^{\Delta} =&p(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}.