Abstract: In the present work, we pay attention to a number of nonlinear Volterra integro-differential equations (VIDEs) with constant time-lag. We define three new Lyapunov functionals (LFs) and employ them to get specific conditions guaranteeing the uniform exponential asymptotic stability (UEAS) of the trivial solutions of the (VIDEs) considered. The results obtained generalize, compliment and improve the existing results in the literature from the cases of the without delay to the more general cases with time-lag.

In this paper, we investigate the instability of solutions to a certain class of nonlinear vector functional differential equations of the eighth order with n-deviating arguments. We employ the Lyapunov-Krasovskii functional approach and base on the Krasovskii criteria to prove two new theorems on the topic. Our results improve certain results in the literature from scalar functional differential equations to their vectorial forms.

This paper deals with a certain third-order non-linear differential equation with multiple deviating arguments. Some sufficient conditions are set up for all solutions and their derivatives to be uniformly bounded.

En este artículo se estudia un tipo de ecuaciones diferenciales no lineales de tercer orden con argumentos de desviación múltiple. Se establecen algunas condiciones suficientes para que todas las soluciones y sus derivadas sean uniformemente acotadas.

In this paper, we improve some boundedness results, which have been obtained with respect to nonlinear differential equations of fifth order without delay, to a certain functional differential equation with constant delay. We give an illustrative example and also verify our main result by means of Liaponov tecnique.

There are given sufficient conditions for the asymptotic stability of the zero solution of equation (1.1) with p = 0 and the boundedness of all solutions of the same equation (1.1), with p <FONT FACE=Symbol>¹</FONT> 0.