Existence of positive periodic solutions for a class of second-order neutral functional differential equations

摘要

In this paper, under some ordered conditions, we investigate the existence of positive omega-periodic solutions for a class of second-order neutral functional differential equations with delayed derivative in nonlinearity of the form (x(t) - cx(t - delta))'' + a(t)g(x(t))x(t) = lambda b(t)f(t, x(t), x(t - tau(1)(t)), x '(t - tau(2)(t))). By utilizing the perturbation method of a positive operator and the fixed point index theory in cones, some sufficient conditions are established for the existence as well as the non-existence of positive omega-periodic solutions.