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Controllability results for functional semilinear differential inclusions in Fréchet spaces. (English) Zbl 1086.34062

The paper is devoted to four types of inclusions in Fréchet spaces. Namely, first- and second-order semilinear functional-differential inclusions as well as semilinear neutral functional-differential inclusions. The main goal of the work consists in the proof of theorems on existence and uniqueness of mild solutions to such inclusions. The authors thereto make use of techniques of noncompactness measures, of semigroup theory as well as of one variety of fixed-points theorems – Frigon’s nonlinear alternative. One of the proved theorems is illustrated with a parabolic neutral type partial inclusion. It should be noted that the word “controllability” in the paper title has a weak relation to the essence of the issue discussed in the work.

MSC:

34K30 Functional-differential equations in abstract spaces
34K25 Asymptotic theory of functional-differential equations
34G25 Evolution inclusions
93B05 Controllability
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