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

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.