Abstract
In this paper, the functional dynamic equation of second order is studied on an arbitrary time scale under milder restrictions without the assumed conditions in the recent literature. The Nehari, Hille, and Ohriska type oscillation criteria of the equation are investigated. The presented results confirm that the study of the equation in this formula is superior to other previous studies. Some examples are addressed to demonstrate the finding.
Highlights
In order to combine continuous and discrete analysis, the theory of dynamic equations on time scales was proposed by Stefan Hilger in [1]
The study of nonlinear dynamic equations is considered in this work because these equations arise in various real-world problems like the turbulent flow of a polytrophic gas in a porous medium, non-Newtonian fluid theory, and in the study of p−Laplace equations
We are interested in the oscillatory behavior of the nonlinear functional dynamic equation of second order with deviating arguments h i∆
Summary
Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt These authors contributed equally to this work. Received: 12 September 2020; Accepted: 23 October 2020; Published: 31 October 2020
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