Oscillation of Forced Nonlinear Neutral Delay Difference Equations of First Order
نویسندگان
چکیده
منابع مشابه
Oscillation of second order nonlinear neutral delay difference equations
In this paper sufficient conditions are obtained for oscillation of all solutions of a class of nonlinear neutral delay difference equations of the form ∆(y(n) + p(n)y(n−m)) + q(n)G(y(n − k)) = 0 under various ranges of p(n). The nonlinear function G,G ∈ C(R,R) is either sublinear or superlinear. Mathematics Subject classification (2000): 39 A 10, 39 A 12
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where (i) {p(n)}, {e(n)} are sequences of real numbers; (ii) {qi(n)}, i= 1,2, are sequences of positive real numbers; (iii) λ, μ are ratios of positive odd integers with 0 < μ < 1 and λ > 1. By a solution of equation (1, i), i= 1,2,3, we mean a nontrivial sequence {x(n)}which is defined for n ≥ n0 ∈ N = {0,1,2, . . .} and satisfies equation (1, i), i = 1,2,3, and n = 1,2, . . . . A solution {x(...
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This paper considers the oscillation problem for forced nonlinear difference equations of the form 0096-3 doi:10 * Co E-m Dxn þ qnf ðxn sÞ 1⁄4 en: We study three cases: qn P 0, qn < 0 and qn is oscillatory. No restriction assumed in known literatures is imposed on the forcing term en. 2006 Elsevier Inc. All rights reserved.
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Oscillation criteria, extended Kamenev and Philos-type oscillation theorems for the nonlinear second order neutral delay differential equation with and without the forced term are given. These results extend and improve the well known results of Grammatikopoulos et. al., Graef et. al., Tanaka for the nonlinear neutral case and the recent results of Dzurina and Mihalikova for the neutral linear ...
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In this paper, we study the forced oscillation of the higher-order nonlinear difference equation of the form m x(n) – p(n)x(n – τ) + q 1 (n) α (n – σ 1) + q 2 (n) β (n – σ 2) = f (n), where m ≥ 1, τ , σ 1 and σ 2 are integers, 0 < α < 1 < β are constants, * (u) = |u| *–1 u, p(n), q 1 (n), q 2 (n) and f (n) are real sequences with p(n) > 0. By taking all possible values of τ , σ 1 and σ 2 into c...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2003
ISSN: 0011-4642,1572-9141
DOI: 10.1023/a:1022975525370