Nonoscillation and positivity of solutions to first order state-dependent differential equations with impulses in variable moments
نویسندگان
چکیده
The state-dependent delay differential equation ẋ(t)+ m ∑ i=1 pi(t)x ( t − (Hix)(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. © 2006 Elsevier Inc. All rights reserved. MSC: 34K45; 34K05
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تاریخ انتشار 2006