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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http://dx.doi.org/10.3934/mbe.2022178 | DOI Listing |
Sci Rep
November 2024
Department of Basic Science, Higher Technological Institute, Sixth of October, Giza, 12573, Egypt.
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.
View Article and Find Full Text PDFMath Biosci Eng
February 2022
Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia.
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.
View Article and Find Full Text PDFJ Inequal Appl
July 2018
3School of Information Science and Engineering, Linyi University, Linyi, P.R. China.
The paper is devoted to the study of oscillation of solutions to a class of second-order half-linear neutral differential equations with delayed arguments. New oscillation criteria are established, and they essentially improve the well-known results reported in the literature, including those for non-neutral differential equations. The adopted approach refines the classical Riccati transformation technique by taking into account such part of the overall impact of the delay that has been neglected in the earlier results.
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