## Existence of positive periodic solutions for non-autonomous functional differential equations.(English)Zbl 1003.34059

The authors discuss the existence of positive periodic solutions to the following first-order functional-differential equation of the form $y'(t)=-a(t)y(t)+\lambda h(t) f(y(t-\tau(t))),$ where $$a(t), h(t)$$ and $$\tau(t)$$ are continuous and nonnegative $$T$$-periodic functions, $$\lambda >0$$ is a constant. Some sufficient conditions are established. A fixed-point theorem due to Krasnoselskij is used to prove the existence of periodic solutions.

### MSC:

 34K13 Periodic solutions to functional-differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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