Abstract
This paper studies the oscillation properties and asymptotic behavior of all solutions of the 2×2 system of second-order half-linear neutral differential equations. Four results are obtained in this research. The first and second results are auxiliary results while the third and fourth results are main results. All possible cases of non-oscillating bounded solutions for this system are estimated and analyzed. It is noted that the parameters that affect the volatility of the solutions are Qi,Ri on the one hand and r1 and r2 on the other hand. For this purpose, and through investigation, it is shown that there are only fourteen possible cases of non-oscillating bounded solutions for this system, so all these cases must be treated, in the first result as well as the second, some new necessary and sufficient conditions were obtained to ensure that there are no non-oscillating bounded solutions in these cases, and thus all possible solutions for this system, if they exist, will be only oscillating solutions and there are no non-oscillating solutions for this type of equations. Some examples are included to illustrate all the results obtained.
Keywords
Asymptotic Behavior, Half linear system, Neutral Differential Equations, Oscillation, Second Order
Subject Area
Mathematics
Article Type
Article
First Page
2002
Last Page
2017
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite this Article
Abdulkarem, Noor Abdulamer; Abed, Taghreed Hussein; Abdulkareem, Farah Abdulameer; and Mohamad, Hussain Ali
(2025)
"Mostly oscillation for a system of half linear neutral differential equations of the second order with several arguments,"
Baghdad Science Journal: Vol. 22:
Iss.
6, Article 23.
DOI: https://doi.org/10.21123/2411-7986.4973