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Acyclicity of solution sets to functional inclusions. (English) Zbl 1012.34011
The first purpose of the authors is to obtain topological properties (compact acyclic, \(R_{\delta}\)) of the fixed-point set of some operators, by using the inverse systems of topological spaces and the limit map technique. Examples illustrating this approach (multivalued Cauchy problems) are also considered.
The second aim of the authors is to prove a multivalued generalization of the Aronszajn theorem [N. Aronszajn, Ann. Math., II. Ser. 43, 730-738 (1942; Zbl 0061.17106)], by using the Browder-Gupta effective approach [F. E. Browder and C. P. Gupta, J. Math. Anal. Appl. 26, 390-402 (1969; Zbl 0176.45401)]. An interesting application to a multivalued boundary value problem conclude the second part of the paper.

MSC:
34A60 Ordinary differential inclusions
47H10 Fixed-point theorems
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