Oscillation of second order nonlinear difference equations with super-linear neutral term

Abstract

In this paper, the authors establish some new conditions for the oscillation of second order nonlinear difference equation of the form ∆ a n ∆ y n + p n y α n−k + q n y β n+1− = 0, where α > 1 and β are ratio of odd positive integers. Examples are provided to illustrate the importance of the main results.

Oscillation criteria for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term

“…Furthermore, the oscillation criteria developed here are novel and add to the findings previously reported in the literature. The neutral coefficient ρ(t) ∈ (0, 1) prevents the results presented in [3,4,11,16,19,27,32,33] from being applicable to our equations (3.1)-(3.3). As a result, our findings constitute a highly valuable addition to the oscillation theory of second-order neutral difference equations with superlinear neutral terms.…”

“…In view of the above observations, the researchers paid attention to the oscillation area for various classes of second-order difference, differential and dynamic equations, see [2,6,7,8,10,12,13,14,15,17,18,21,24,25,26,29,31] and the references cited therein. As far as secondorder difference equations with positive superlinear neutral terms are considered, not many results are known about the oscillation, see [3,4,11,16,19,27,32,33].…”