Abstract
In this paper, we study the topological properties to a C^{0}-solution set of impulsive evolution inclusions. The definition of C^{0}-solutions for impulsive functional evolution inclusions is introduced. The R_{delta}-property of C^{0}-solution set is studied for compact as well as noncompact semigroups on compact intervals. Applying the inverse limit method, the R_{delta}-structure on noncompact intervals is obtained.
Highlights
1 Introduction Impulsive differential equations and inclusions act as excellent tools to model the real world phenomena exhibiting instantaneous change in state variables
In [13], Cardinali et al focused on the compactness of the set of mild solutions to semilinear impulsive evolution differential inclusions and obtained the existence of mild solutions for semilinear impulsive evolution differential inclusion on noncompact domains in the case of a noncompact semigroup
Gabor et al [20, 21] showed that the solution set of impulsive functional differential inclusions is an Rδ-set on compact intervals, and extended their work to the half-line by using the inverse limit method, when the semigroup is noncompact
Summary
Impulsive differential equations and inclusions act as excellent tools to model the real world phenomena exhibiting instantaneous change in state variables. Lemma 3.3 Let E∗ be uniformly convex and A be an m-dissipative operator generating a compact semigroup.
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