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NEW OSCILLATION CRITERIA FOR H-DIFFERENCE EQUATION WITH OSCILLATORY PERIODIC COEFFICIENTS
  • Yasar Bolat,
  • REYHAN GOKTEKE
Yasar Bolat
Kastamonu Universitesi

Corresponding Author:ybolat@kastamonu.edu.tr

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REYHAN GOKTEKE
Kastamonu Universitesi
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Abstract

In this manuscript new oscillation criteria are given for solutions of h-order delay difference equation in the form ∆ E n + p n E n − α = 0 . Here, four cases of p are considered; for α∈N , as oscillatory periodic sequences with periods 2 α,(2 α+1) and ( α+1) , and a quickly oscillating sequence such that p n p n + 1 < 0 . It is well known that coefficient functions has a very important role in the behavior of the solutions of an equation. The coefficients sequence p has been considered as positive sequences in all oscillation criteria so far. But It is considered as a oscillatory periodic sequences and quickly oscillatory sequences for the first time in this study. We use a new technique to prove our results. Also some examples are provided to demonstrate the effectiveness of the main results.
08 Sep 2024Submitted to Mathematical Methods in the Applied Sciences
09 Sep 2024Submission Checks Completed
09 Sep 2024Assigned to Editor
18 Sep 2024Review(s) Completed, Editorial Evaluation Pending
19 Sep 2024Reviewer(s) Assigned