EXISTENCE OF PERIODIC SOLUTIONS FOR NEUTRAL NONLINEAR DIFFERENTIAL EQUATIONS WITH VARIABLE DELAY

We use a variation of Krasnoselskii fixed point theorem introduced by Burton to show that the nonlinear neutral differential equation x'(t) = -a(t)x(3)(t) + c(t)x' (t - g(t)) + G(t, x(3)(t - g(t)) has a periodic solution. Since this equation is nonlinear, the variation of parameters can not be applied directly; we add and subtract a linear term to transform the differential into an equivalent integral equation suitable for applying a fixed point theorem. Our result is illustrated with an example.