Criteria for oscillation of noncanonical superlinear half-linear dynamic equations

Taher S Hassan; Clemente Cesarano; Mouataz Billah Mesmouli; Y A Madani; Amir Abdel Menaem; Ayékotan M J Tchalla; Belal A Glalah

doi:10.1038/s41598-024-69922-2

Criteria for oscillation of noncanonical superlinear half-linear dynamic equations

Sci Rep. 2024 Nov 16;14(1):28360. doi: 10.1038/s41598-024-69922-2.

Authors

Taher S Hassan^{1

2

3}, Clemente Cesarano³, Mouataz Billah Mesmouli¹, Y A Madani¹, Amir Abdel Menaem⁴, Ayékotan M J Tchalla⁵, Belal A Glalah⁶

Affiliations

¹ Department of Mathematics, College of Science, University of Ha'il, Ha'il, 2440, Saudi Arabia.
² Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt.
³ Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy.
⁴ Department of Automated Electrical Systems, Ural Power Engineering Institute, Ural Federal University, Yekaterinburg, Russia, 620002.
⁵ Département de Mathématiques , Faculté Des Sciences, Université de Lomé, 01 BP 1515, Lomé, Togo. atchalla@univ-lome.tg.
⁶ Department of Basic Science, Higher Technological Institute, Sixth of October, Giza, 12573, Egypt.

Abstract

This article comes up with criteria to make sure that the solutions to superlinear, half-linear, and noncanonical dynamic equations oscillate in both advanced and delayed cases; these criteria are comparable to the Hille-type and Ohriska-type criteria for the canonical nonlinear dynamic equations; and also these results solve an open problem in many existing works in the literature on dynamic equations. To demonstrate the importance of the results, some examples have been introduced.

Keywords: Dynamic equation; Nonlinear; Oscillation behavior; Second-order; Time scales.