In the present paper we study the approximate solutions of a certain difference-differential equation under the given initial conditions. The well known Gronwall-Bellman integral inequality is used to establish the results. Applications to a Volterra type difference-integral equation are also given.

We address some questions concerning a class of differential variational inequalities with finite delays. The existence of exponential decay solutions and a global attractor for the associated multivalued semiflow is proved.

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.

In this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative conditions on the nonlinear term,we define a non-autonomous dynamical system and prove the existence of a pullback attractor for such system as well. Both multivalued and single-valued cases are considered.