Existence of positive solutions of halflinear delay differential equation (Q855435)

Using the method of generalized Riccati equation and the Schauder-Tikhonov fixed point theorem, the authors present sufficient conditions for the existence of positive solutions of the delay differential equation \[ \left[| x'(t)|^{\alpha-1}x'(t)\right]'+\sum_{i=1}^{n}p_i(t) | x(t-\tau_i(t))|^{\alpha-1}x(t-\tau_i(t))=0 \] for \(t\geq t_0\) and \(\alpha>0\).