In this paper, oscillation and asymptotic behavior of three-dimensional third-order delay systems are discussed. Some sufficient conditions are obtained to ensure that every solution of the system is either oscillatory or nonoscillatory and converges to zero or diverges as
t
goes to infinity. A special technique is adopted to include all possible cases for all nonoscillatory solutions (NOSs). The obtained results included illustrative examples.
In this research, the oscillation and the asymptotic behavior of a half-linear three-dimensional neutral differential system of the second order have been studied, where all the non-oscillating solutions have been classified into 16 different classes, and then sufficient conditions were given to prove that most of these classes are inactive and non-occurring, that is empty, as for the rest classes, it has been proven that all its bounded solutions, either oscillating or non-oscillating, converge to zero when , and all unbounded solutions, are either oscillating or non-oscillating, goes to as . Some examples are given to illustrate the obtained results
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.