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Oscillation of Second Order Nonlinear Delay Damped Difference Equations

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Abstract

Some new oscillation criteria for nonlinear delay difference equation with damping

$$ \begin{array}{*{20}c} {{\Delta ^{2} x_{n} + p_{n} \Delta x_{n} + F{\left( {n,x_{{n - r}} ,\Delta x_{{n - \sigma }} } \right)} = 0,}} & {{n = 0,1,2,...,}} \\ \end{array} $$
((∗))

are given. Our results partially solve the open problem posed in [Math. Bohemica, 125 (2000), 421– 430]. Also, we will establish some new oscillation criteria for special cases of (∗), which improve some of the well–known results in the literature.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

    S. H. Saker

  2. Department of Mathematics, Ocean University of China, Qingdao 266071, P. R. China

    B. G. Zhang

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  1. S. H. Saker
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  2. B. G. Zhang
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Correspondence to S. H. Saker.

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Saker, S.H., Zhang, B.G. Oscillation of Second Order Nonlinear Delay Damped Difference Equations. Acta Math Sinica 23, 715–722 (2007). https://doi.org/10.1007/s10114-005-0792-1

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