In the paper we study the existence of nonoscillatory solutions of the system $x_i^{\left(n\right)}\left(t\right)={\sum }_{j=1}^2{p}_{ij}\left(t\right)f_{ij}\left(x_j\left(h_{ij}\left(t\right)\right)\right),n\ge 2,i=1,2$, with the property $li{m}_{t\to \infty }{x}_i\left(t\right)/t^{k_i}=const\ne 0$ for some $k_i\in \{1,2,...,n-1\},i=1,2$. Sufficient conditions for the oscillation of solutions of the system are also proved.

The aim of this paper is to study asymptotic properties of the solutions of the third order delay differential equation $${\left(\frac{1}{r\left(t\right)}{y}^{\text{'}}\left(t\right)\right)}^{\text{'}\text{'}}-p\left(t\right)y^{\text{'}}\left(t\right)+g\left(t\right)y\left(\tau \left(t\right)\right)=0.*$$ 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: $\Psi$-boundedness and $\Psi$-asymptotic equivalence, where $\Psi$ is a complex continuous nonsingular $n\times n$ matrix. The $\Psi$-asymptotic equivalence of linear differential systems $y^{\text{'}}=A\left(t\right)y$ and $x^{\text{'}}=A\left(t\right)x+B\left(t\right)x$ is proved when the fundamental matrix of $y^{\text{'}}=A\left(t\right)y$ is $\Psi$-bounded.

Asymptotic representations of some classes of solutions of nonautonomous ordinary differential $n$-th order equations which somewhat are close to linear equations are established.

This paper is concerned with the existence and uniqueness of asymptotically almost automorphic solutions to differential equations with piecewise constant argument. To study that, we first introduce several notions about asymptotically almost automorphic type functions and obtain some properties of such functions. Then, on the basis of a systematic study on the associated difference system, the existence and uniqueness theorem is established. Compared with some earlier results, we do not assume...

In this paper, we prove and discuss averaging results for ordinary differential equations perturbed by a small parameter. The conditions we assume on the right-hand sides of the equations under which our averaging results are stated are more general than those considered in the literature. Indeed, often it is assumed that the right-hand sides of the equations are uniformly bounded and a Lipschitz condition is imposed on them. Sometimes this last condition is relaxed to the uniform continuity in...