Existence of positive solutions of halflinear delay differential equation

In this paper we consider the halflinear delay differential equation[|x′(t)|α−1x′(t)]′+∑i=1npi(t)|x(t−τi(t))|α−1x(t−τi(t))=0 for t⩾t0t⩾t0 and α>0α>0. Using the method of generalized Riccati equation, we give conditions for the existence of positive solutions.