Differential inclusions with state-dependent impulses on the half-line: New Fréchet space of functions and structure of solution sets

An RδRδ-structure of solution sets to some classes of impulsive differential inclusions with variable impulse times on the half-line is shown. Sufficient conditions on barriers are discussed in detail. They imply two different techniques: the inverse limit method and the one based on a definition of RδRδ-sets and used in a new suitable Fréchet function space.