## Two periodic solutions of second-order neutral functional differential equations.(English)Zbl 1118.34063

The authors investigate the existence, multiplicity and nonexistence of positive periodic solutions for the following second-order neutral functional differential equations $(x(t)-cx(t-\delta))''+a(t)x(t)=\lambda b(t)f(x(t-\tau(t))),$ where $$\lambda$$ is a positive parameter, $$c$$ and $$\delta$$ are constants and $$| c| \not=1$$. The criteria essentially depend on the limits of the function $$f(u)/u$$ as $$u$$ tends to zero or infinity. The approach is based on the Krasnoselskii fixed point theorem.

### MSC:

 34K13 Periodic solutions to functional-differential equations 34K40 Neutral functional-differential equations 47H10 Fixed-point theorems

### Keywords:

Krasnoselskii fixed point theorem
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### References:

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