Upper and weak-lower semicontinuity of pullback attractors to impulsive evolution processes

Abstract

In this paper, following the work done in [11], we deal with the upper and weak-lower semicontinuity of pullback attractors for impulsive evolution processes. We first deal with the upper semicontinuity, presenting the abstract theory and applying it to uniform perturbations of a nonautonomous integrate-and-fire neuron model. We also present the abstract theory of weak-lower semicontinuity, and finish with an improvement of [11,Subsection 4.2], proving an invariance property for impulsive pullback omega-limits with weaker assumptions.