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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
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