R_δ-structure of solutions set for a vector evolution inclusions defined on right half-line

In this paper, we deal with the topological structure of a first order vector differential inclusion defined on right half-line. Under some general growth conditions, the R_δ structure of continue solution set for Cauchy problem on compact interval is investigated. Then by the inverse limit method, the R_δ structure is also obtained on noncompact interval. Further, using the related results of structure, we obtain the existence and topological structure of solution set for some nonlocal problems. Subsequently a optimal dual control problem is considered and an R_δ structure of attainable set based on the proven results is obtained.