Structure of the solution set to impulsive functional differential inclusions on the half-line (Q1928844)

The authors use the inverse system method initiated and developed in earlier papers to study the topological structure of fixed point sets of operators in function spaces. It is observed that differential problems on a noncompact interval can be reformulated as fixed point problems in Fréchet spaces and these are inverse limits of Banach spaces when the differential problems are considered on compact intervals. As the existence of mild solutions for impulsive Cauchy semilinear differential inclusions on noncompact intervals has been obtained in an earlier work, in this paper, the authors state and prove the compactness of the solution set for this problem. They further prove that the set is an \(R_ \delta\) set. This information can be used to check whether the translation operator, employed to detect periodic solutions, is admissable or not and fixed point theory methods can be applied.