Nonoscillation and positivity of solutions to first order state-dependent differential equations with impulses in variable moments

The state-dependent delay differential equation with state-dependent impulses is under consideration. Sufficient conditions for positivity of solutions to the Cauchy and periodic problems as well as conditions for positivity of solutions to the problem with a condition on the right end of the interval [0,ω] are given. Sufficient conditions for nonoscillation of solutions to the homogeneous equation (f=0, φ=0) on the half-line are formulated.