On Attractors of Generalized Semiflows with Impulses

This paper is devoted to the study of global attractors for problems with state-dependent impulses and possible nonuniqueness of solutions. We provide the criteria under which there exists the global attractor, being on one hand an invariant set, and on the other hand given by the difference of the minimal compact attracting set and the impulsive set M. The new condition (T) used to get the global attractor invariance is discussed and compared with other conditions used in literature for impulsive problems. The theory is illustrated by several examples.