Oscillation of solutions of impulsive neutral difference equations with continuous variable

Gengping Wei and Jianhua Shen

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-7

Abstract:

We obtain sufficient conditions for oscillation of all solutions of the neutral impulsive difference equation with continuous variable Δ τ ( y ( t ) + p ( t ) y ( t − m τ ) ) + Q ( t ) y ( t − l τ ) = 0 , t ≥ t 0 − τ , t ≠t k , y ( t k + τ ) − y ( t k ) = b k y ( t k ) , k ∈ ℕ ( 1 ) , where Δ τ denotes the forward difference operator, that is, Δ τ z ( t ) = z ( t + τ ) − z ( t ) , p ( t ) ∈ C ( [ t 0 − τ , ∞ ) , ℠) , Q ( t ) ∈ C ( [ t 0 − τ , ∞ ) , ( 0 , ∞ ) ) , m , l are positive integers, τ > 0 and b k are constants, 0 ≤ t 0 < t 1 < t 2 < ⋯ < t k < ⋯ with lim k → ∞ t k = ∞ .

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:034232

DOI: 10.1155/IJMMS/2006/34232

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