Geodesic
On the topological dimension of the solutions sets for some classes of operator and differential inclusions
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 22 (2002) no. 1, pp. 17-32.

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In the present paper, we give the lower estimation for the topological dimension of the fixed points set of a condensing continuous multimap in a Banach space. The abstract result is applied to the fixed point set of the multioperator of the form = S _F where _F is the superposition multioperator generated by the Carathéodory type multifunction F and S is the shift of a linear injective operator. We present sufficient conditions under which this set has the infinite topological dimension. In the last section of the paper, we consider the applications of the solutions sets for Cauchy and periodic problems for semilinear differential inclusions in a Banach space.
Keywords: solutions set, fixed points set, topological dimension, multivalued map, condensing map, topological degree, differential inclusion, periodic problem 
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Bader, Ralf; Gel'man, Boris; Kamenskii, Mikhail; Obukhovskii, Valeri. On the topological dimension of the solutions sets for some classes of operator and differential inclusions. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 22 (2002) no. 1, pp. 17-32. http://geodesic.mathdoc.fr/item/DMDICO_2002_22_1_a1/

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