Two periodic solutions of second-order neutral functional differential equations (Q868816)

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.