On Positivity of Solutions of Delayed Differential Equation with State Dependent Impulses

We consider the delay differential equation x(t) + p(t)x(t - ?(t)) = f(t), t?[0,?) x(?) = ?(?), ?<0 with state dependent impulses. We give sufficient conditions for positivity of solutions of the Cauchy and periodic problems as well as conditions for positivity of solutions of the initial problem with a condition on the right end of the interval [0, ?]. We also formulate sufficient conditions for nonoscillation of solutions of the homogeneous equation (f = 0, ? = 0) on the halfline.