Geodesic
Topological properties of the solution set of a class of nonlinear evolutions inclusions
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 3, pp. 409-424

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In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field $F(t,x)$, we are able to show that the solution set is in fact an $R_\delta $-set. Finally some applications to infinite dimensional control systems are also presented.
Classification : 34G20, 34H05, 35B30, 35B37, 35R45, 49A20, 49J24
Keywords: $R_\delta $-set; homotopic; contractible; evolution triple; evolution inclusion; compact embedding; optimal control 
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     author = {Papageorgiou, Nikolaos S.},
     title = {Topological properties of the solution set of a class of nonlinear evolutions inclusions},
     journal = {Czechoslovak Mathematical Journal},
     pages = {409--424},
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     volume = {47},
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     zbl = {0898.35011},
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Papageorgiou, Nikolaos S. Topological properties of the solution set of a class of nonlinear evolutions inclusions. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 3, pp. 409-424. http://geodesic.mathdoc.fr/item/CMJ_1997__47_3_a2/