Taiwanese Journal of Mathematics

CONTROLLABILITY FOR A CLASS OF DEGENERATE FUNCTIONAL DIFFERENTIAL INCLUSIONS IN A BANACH SPACE

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

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Abstract

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

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

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405142

Digital Object Identifier
doi:10.11650/twjm/1500405142

Mathematical Reviews number (MathSciNet)
MR2459820

Zentralblatt MATH identifier
1166.93005

Subjects
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]

Keywords
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

Citation

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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