Existence of positive solutions for delay differential equations with impulses (Q1363597)

The authors study the linear delay differential equation with impulses \[ \begin{aligned} &x'(t)+ \sum_{i=1}^n p_i (t) x(t-\tau_i) =0, \quad t\neq t_k,\\ &x(t_k^+) - x(t_k) = b_k x(t_k), \quad k=1,2,\dots\end{aligned}\tag{1} \] Some sufficient conditions for existence of positive solutions and a comparison theorem are obtained. The approach is based on establishing the equivalence of the existence of positive solutions of (1) and solutions of an integral equation.