Abstract

By using the Riccati transformation and mathematical analytic methods, some sufficient conditions are obtained for oscillation of the second-order quasilinear neutral delay difference equations $$ \Delta [r_n |\Delta z_n |^{\alpha - 1} \Delta z_n ] + q_n f(x_{n - \sigma } ) = 0, $$ where zn = xn + pnxn-τ\( \sum\limits_{n = 0}^\infty {1/r_n^{\tfrac{1} {\alpha }} } < \infty \).

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