Topological structure of solution sets for impulsive differential inclusions in Fréchet spaces |
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| Authors: | Smaï l Djebali,Abdelghani Ouahab |
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| Affiliation: | a Laboratory of EDP & HM, Department of Mathematics, E.N.S., PB 92, 16050 Kouba, Algiers, Algeriab Institute of Mathematics, Kazimierz Wielki University, Bydgoszcz, Polandc Schauder Center for Nonlinear Studies, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Polandd Laboratory of Mathematics, Sidi-Bel-Abbès University, PB 89, 22000 Sidi-Bel-Abbès, Algeria |
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| Abstract: | In this paper, we consider the existence of solutions as well as the topological and geometric structure of solution sets for first-order impulsive differential inclusions in some Fréchet spaces. Both the initial and terminal problems are considered. Using ingredients from topology and homology, the topological structures of solution sets (closedness and compactness) as well as some geometric properties (contractibility, acyclicity, AR and Rδ) are investigated. Some of our existence results are obtained via the method of taking the inverse system limit on noncompact intervals. |
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| Keywords: | 34A37 34A60 34K30 34K45 47H10 54C60 54C65 55M15 |
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