## Taiwanese Journal of Mathematics

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

#### 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

https://projecteuclid.org/euclid.twjm/1500405142

Digital Object Identifier
doi:10.11650/twjm/1500405142

Mathematical Reviews number (MathSciNet)
MR2459820

Zentralblatt MATH identifier
1166.93005

#### 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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