Taiwanese Journal of Mathematics


Y. C. Liou, V. Obukhovskii, and J. C. Yao

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We study the controllability problem for a system governed by a degenerate semilinear functional differential inclusion in a Banach space with infinite delay. Notice that we are not assuming that the generalized semigroup generated by the linear part of inclusion is compact. Instead we suppose that the multivalued nonlinearity satisfies the regularity condition expressed in terms of the Hausdorff measure of noncompactness. It allows to obtain the general controllability principle in the terms of the topological degree theory for condensing multivalued operators. Two realizations of this principle are considered.

Article information

Taiwanese J. Math., Volume 12, Number 8 (2008), 2179-2200.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 93B05: Controllability 34A60: Differential inclusions [See also 49J21, 49K21]
Secondary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 34K35: Control problems [See also 49J21, 49K21, 93C23] 47H04: Set-valued operators [See also 28B20, 54C60, 58C06] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

controllability functional differential inclusion degenerate differential inclusion Banach space infinite delay phase space mild solution measure of noncompactness fixed point topological degree multivalued map condensing map


Liou, Y. C.; Obukhovskii, V.; Yao, J. C. CONTROLLABILITY FOR A CLASS OF DEGENERATE FUNCTIONAL DIFFERENTIAL INCLUSIONS IN A BANACH SPACE. Taiwanese J. Math. 12 (2008), no. 8, 2179--2200. doi:10.11650/twjm/1500405142. https://projecteuclid.org/euclid.twjm/1500405142

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