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Periodic solutions for some nonlinear differential equations of neutral type. (English) Zbl 0735.34066
The main results of the paper deal with the existence of periodic solutions of the problem $x'(t)+ax'(t-\tau)=f(t,x(t))$, $x$ $2\pi$- periodic, where $f:\bbfR\times\bbfR\to\bbfR$ is Carathéodory, $f(\cdot,y)$ is $2\pi$-periodic for $x$, $a\in\bbfR$ and $\tau\in(0,2\pi)$. All existence theorems are considered corresponding to one from the following two cases $\vert a\vert<1$ and $\vert a\vert=1$.

##### MSC:
 34K40 Neutral functional-differential equations 34C25 Periodic solutions of ODE 34K99 Functional-differential equations
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##### References:
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