On the existence of asymptotically decaying positive solutions of second order neutral differential equations

AbstractThe existence of positive solutions of second order neutral differential equation (x(t) − cx(t − τ))″ + p(t)x(g(t)) = 0, t ⩾ t0 (∗) is investigated. Some sufficient conditions are given for the existence of positive solutions with asymptotic decay of (∗) for the cases of constant sign and nonconstant sign of coefficients. It also is shown that one of these sufficient conditions is necessary