On the delay differential equation y'(x) = ay(τ(x)) + by(x)

Čermák, Jan

doi:10.4064/ap-71-2-161-169

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Cited by 6 publications

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“…Asymptotic properties of solutions of homogeneous equations with constant coefficients and unbounded delays have been investigated also in [3]. Our aim is to unify and generalize some results concerning (1.2), (1.3), (1.4) and other related equations.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behaviour of solutions of some differential equations with an unbounded delay

Čermák¹

1999

Proceedings of the 6'th Colloquium on the Qualitative Theory of Differential Equations (August 10--14, 1999, Szeged, Hungary) E

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We investigate the asymptotic properties of all solutions of the functional differential equatioṅ x(t) = p(t)[x(t) − kx(t − τ (t))] + q(t), t ∈ I = [t 0 , ∞), where k = 0 is a scalar and τ (t) is an unbounded delay. Under certain restrictions we relate the asymptotic behaviour of the solutions x(t) of this equation to the behaviour of a solution ϕ(t) of the auxiliary functional nondifferential equation ϕ(t) = |k| ϕ(t − τ (t)), t ∈ I.

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Section: Introductionmentioning

confidence: 99%