Kumar S. Vidhyaa, Ethiraju Thandapani, Jehad Alzabut, Abdullah Ozbekler
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.
DOI: https://doi.org/10.58997/ejde.2023.45
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Kumar S. Vidhyaa Easwari Engineering College Department of Mathematics Ramapuram, Chennai - 6000089, India email: vidyacertain@gmail.com |
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Ethiraju Thandapani Ramanujam Institute for Advanced Study in Mathematics University of Madras Chennai - 600005, India email: ethandapani@yahoo.co.in |
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Jehad Alzabut Department of Mathematics and Sciences Prince Sultan University 11586 Riyadh, Saudi Arabia email: jalzabut@psu.edu.sa |
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Abdullah Özbekler Department of Mathematics Atilim University 06830 Incek, Ankara, Turkey email: aozbekler@gmail.com, abdullah.ozbekler@atilim.edu.tr |
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