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Oscillations for even-order neutral difference equations

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Abstract

Consider the even-order neutral difference equation

$$(*)\Delta ^m (x_n - p_n g)(x_{n\_k} )) - q_n h(x_{n\_l} ) = 0,n = 0,1,2,...$$

where Δ is the forward difference operator,m is even, {−p n,qn are sequences of nonnegative real numbers,k, l are nonnegative integers,g(x),h(x) ∈ C(R, R) withxg(x) > 0 forx ≠ 0. In this paper, we obtain some linearized oscillation theorems of (*) forp n ∈ (−∞, 0) which are discrete results of the open problem by Gyori and Ladas.

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Authors and Affiliations

  1. Deaprtment of Applied Mathematics, Hunan University, 410082, Changsha, Hunan, P. R. China

    Zhan Zhou & Jianshe Yu

  2. Institute of International Business, Hunan University, 410082, Changsha, Hunan, P. R. China

    Guanglong Lei

Authors
  1. Zhan Zhou
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  2. Jianshe Yu
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  3. Guanglong Lei
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Correspondence to Zhan Zhou.

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The Project Supported by NNSF of China

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Zhou, Z., Yu, J. & Lei, G. Oscillations for even-order neutral difference equations. Korean J. Comput. & Appl. Math. 7, 601–610 (2000). https://doi.org/10.1007/BF03012271

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  • DOI: https://doi.org/10.1007/BF03012271

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