Attractors of impulsive dissipative semidynamical systems

In this paper, we consider a class of dissipative semidynamical systems with impulses. First, we study the connectedness of Levinsonʼs center of a compact dissipative system with impulses. Second, we define some types of attractors for dissipative systems and we study results which relate attractors and dissipative systems (point, bounded and compact). Finally, we apply our results for a general impulsive autonomous system and for a nonlinear reaction–diffusion equation of type u′−Δu+g(u)=f with impulse condition.