Existence of asymptotic solutions of second order neutral differential equation with multiple delays

Abstract

The existence of positive solutions of second order neutral differential equation of the form [x(t)−cx(t−h)]′​′+∑i=1mpi(t)x[gi(t)]=0, t≥t0,                                          (A) is investigated. Some sufficient conditions are given for the existence of positive solutions with asymptotic decay of (A). Examples are presented to illustrate the results.