Oscillation result for half-linear delay difference equations of second-order

Chinnasamy Jayakumar; Shyam Sundar Santra; Dumitru Baleanu; Reem Edwan; Vediyappan Govindan; Arumugam Murugesan; Mohamed Altanji; Chinnasamy Jayakumar; Shyam Sundar Santra; Dumitru Baleanu; Reem Edwan; Vediyappan Govindan; Arumugam Murugesan; Mohamed Altanji

doi:10.3934/mbe.2022178

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 4: 3879-3891. doi: 10.3934/mbe.2022178

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Oscillation result for half-linear delay difference equations of second-order

1.
Department of Mathematics, Mahendra Arts & Science College (Autonomous), Kalipatti, Namakkal Dt., Tamil Nadu, India
2.
Department of Mathematics, JIS College of Engineering, Kalyani 741235, India
3.
Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University Ankara, 06790 Etimesgut, Turkey
4.
Instiute of Space Sciences, Magurele-Bucharest, 077125 Magurele, Romania
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, Republic of China
6.
College Of Science And arts, Al-Ola, Taibah University, Al madinah Al Munawwarahn 344, Saudi Arabia
7.
Department of Mathematics, Dmi St John The Baptist University, 800-Central Africa, Malawi
8.
Department of Mathematics, Government Arts College (Autonomous), Salem - 636007, Tamil Nadu, India
9.
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia

Received: 25 December 2021 Revised: 22 January 2022 Accepted: 03 February 2022 Published: 10 February 2022

In this paper, we obtain the new single-condition criteria for the oscillation of second-order half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results.
- oscillation,
- non-oscillation,
- second-order,
- delay,
- half-linear,
- difference equations
Citation: Chinnasamy Jayakumar, Shyam Sundar Santra, Dumitru Baleanu, Reem Edwan, Vediyappan Govindan, Arumugam Murugesan, Mohamed Altanji. Oscillation result for half-linear delay difference equations of second-order[J]. Mathematical Biosciences and Engineering, 2022, 19(4): 3879-3891. doi: 10.3934/mbe.2022178

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Abstract

In this paper, we obtain the new single-condition criteria for the oscillation of second-order half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results.

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