Improved oscillation criteria for second order nonlinear delay difference equations with non-positive neutral term

In this paper, we present some oscillation criteria for second order nonlinear delay difference equation with non-positive neutral term of the form ∆(an (∆zn )α )+qn f(xn-σ) )=0, n>no >0, where zn - xn - pn xn-r, and α is a ratio of odd positive integers. Examples are provided to illustrate the results. The results obtained in this paper improve and complement to some of the existing results.

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Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.