Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 45, pp. 1-12.

Title: Oscillation criteria for non-canonical second-order nonlinear delay difference equations with a superlinear neutral term
       
Authors: Kumar S. Vidhyaa (Easwari Engineering College, Ramapuram, Chennai, India)
         Ethiraju Thandapani (University of Madras, Chennai, India)
         Jehad Alzabut (Prince Sultan Univ., Riyadh, Saudi Arabia)
         Abdullah Ozbekler (Atilim Univ., Ankara, Turkey)

Abstract: 
We obtain oscillation conditions for non-canonical second-order nonlinear
delay difference equations with a superlinear neutral term. To cope with
non-canonical types of equations, we propose new oscillation criteria for the main
equation when the neutral coefficient does not satisfy any of the conditions that
call it to either converge to $0$ or $\infty$.
Our approach differs from others in that we first turn into the non-canonical
equation to a canonical form and as a result, we only require one condition to weed
out non-oscillatory solutions in order to induce oscillation.
The conclusions made here are  new and have been condensed significantly from
those found in the literature. For the sake of confirmation, we provide examples
that cannot be included in earlier works.

Submitted April 24, 2023. Published June 29, 2023.
Math Subject Classifications: 9A103, 34N05.
Key Words: non-canonical; difference equation; superlinear neutral term.