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Periodic solutions of neutral nonlinear system of differential equations with functional delay. (English) Zbl 1118.34057
Summary: We study the existence of periodic solutions of the nonlinear neutral system of differential equations of the form $\frac{d}{dt}x(t)=A(t)x(t)+ \frac{d}{dt} Q(t,x(t-g(t)))+G(t,x(t),x(t-g(t))).$ We use the fundamental matrix solution of $y'=A(t)y$ and convert the given neutral differential equation into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii’s fixed-point theorem to show the existence of a periodic solution of this neutral differential equation. We also use the contraction mapping principle to show the existence of a unique periodic solution of the equation.

##### MSC:
 34K13 Periodic solutions to functional-differential equations 34K40 Neutral functional-differential equations
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##### References:
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