ICPAM-VAN 2022, Van, Turkey, 22 - 23 June 2022, pp.91
This paper considers a certain class of nonlinear vector differential equations of second-order. Qualitative properties of solutions of the considered equations called stability, asymptotic stability, uniform stability, boundedness and uniformly boundedness of solutions are investigated. Eight new theorems related to the mentioned qualitative concepts are proved by using the second method of Lyapunov. Examples are given to show applicability of the results. By this paper, we generalize and improve some results that are available in the literature.