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Periodic solutions for a neutral nonlinear dynamical equation on a time scale. (English) Zbl 1096.34057

Summary: Let 𝕋 be a periodic time scale. We use a fixed-point theorem due to Krasnosel’skiĭ to show that the nonlinear neutral dynamic system with delay

x Δ (t)=-a(t)x σ (t)+c(t)x Δ (t-k)+qt , x ( t ) , x ( t - k ),t𝕋,

has a periodic solution. We assume that k is a fixed constant if 𝕋= and is a multiple of the period of 𝕋 if 𝕋. Under a slightly more stringent inequality, we show that the periodic solution is unique using the contraction mapping principle.

34K40Neutral functional-differential equations
34K13Periodic solutions of functional differential equations
39A12Discrete version of topics in analysis