Invariance properties in the theory of differential equations with time delay and applications

Não disponívelThis work is essentially diuided in two parts. In the first part we introduce the concept of ínvariant set with respect to a nonautonomous delay equation (I) y(t) = P(t, yt). Consider the perturbed equation (2) x(t) = P(t, xt) + Q(t, xt) + S(t, xt) where Q and are \"small\" perturbations in a sence specified in this work. With respect to the concept of invariante, as introduced in the first part, the following property holdes: The ω-limit set of every solution x(t) of (2), bounded in the future, is invariant with respect to (1). In the second part, the following application of the above mentioned theory is done: Consider the equations (I) x + f(t, x, x) + g(x) = 0 (II) x + f(t, x, x) + g(x) + h(t, x, x) = 0 By using the concept of invariance with respect to (I), we obtain, under certain assumptions on f, g and h, some stability results concerning equation (II)