Abstract
The state-dependent delay differential equation x ˙ ( t ) + ∑ i = 1 m p i ( t ) x ( t − ( H i x ) ( t ) ) = f ( t ) , t ∈ [ 0 , ∞ ) , x ( ξ ) = φ ( ξ ) , ξ < 0 , 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.
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