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Oscillations for even-order neutral difference equations

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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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Author information

Correspondence to Zhan Zhou.

Additional information

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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AMS Mathematics Subject Classification

  • 39A10
  • 39A12

Key words and phrases

  • Linearized oscillation
  • even-order
  • neutral difference equations