The aim of this paper is to study asymptotic properties of the solutions of the third order delay differential equation Using suitable comparison theorem we study properties of Eq. () with help of the oscillation of the second order differential equation.
In this paper new generalized notions are defined: -boundedness and -asymptotic equivalence, where is a complex continuous nonsingular matrix. The -asymptotic equivalence of linear differential systems and is proved when the fundamental matrix of is -bounded.
Asymptotic representations of some classes of solutions of nonautonomous ordinary differential -th order equations which somewhat are close to linear equations are established.
Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by , where is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.