Three periodic solutions of nonlinear neutral functional differential equations (Q933564)

The present paper is concerned with the existence of periodic solutions to a class of nonlinear neutral differential equations of the form \[ (x(t)-cx(t-\delta))'= a(t) g(x(t))x(t) -\lambda b(t) f(t,x(t-\tau (t))), \] where \(\lambda\) is a parameter, \(c,d\) are constants and \(| c| \not =1\). The approach is to use a fixed point theorem due to Leggett-Williams. Under some conditions, at least three positive \(\omega\)-periodic solutions have been shown to exist.