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Periodic solutions for differential equations with state-dependent delay and positive feedback. (English) Zbl 1028.34062
The author explores the differential equation with state-dependent delay $\dot{x}(t)=\mu x(t)+f(x(t-r)),\quad r=r(x(t)),$ where $$\mu>0$$, $$f$$ and $$r$$ are smooth real functions with $$r(0)=1$$ and $$f'(0)>0$$. It is proved that the delay differential equation admits a nontrivial periodic orbit and a homoclinic orbit connecting $$0$$ to the periodic orbit. The paper is well written and involves some interesting techniques.

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