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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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