Bulletin of the Belgian Mathematical Society - Simon Stevin

Stability of solutions to integro-differential equations in Hilbert spaces

Jian-Hua Chen, Jin Liang, and Ti-Jun Xiao

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Abstract

In this paper, we investigate the uniform exponential stability of solutions to abstract integro-differential equations in Hilbert spaces by the theory of operator semigroups and Laplace transforms of vector-valued functions. New criterions are given based on the growth property of associated vector-valued functions on the right half plane. Examples are presented to illustrate our results.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 5 (2011), 781-792.

Dates
First available in Project Euclid: 13 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1323787166

Digital Object Identifier
doi:10.36045/bbms/1323787166

Mathematical Reviews number (MathSciNet)
MR2918645

Zentralblatt MATH identifier
1232.34106

Subjects
Primary: 34G10: Linear equations [See also 47D06, 47D09]
Secondary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]

Keywords
Integro-differential equation Exponential stability $C_0$-semigroup Hilbert space

Citation

Chen, Jian-Hua; Liang, Jin; Xiao, Ti-Jun. Stability of solutions to integro-differential equations in Hilbert spaces. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 5, 781--792. doi:10.36045/bbms/1323787166. https://projecteuclid.org/euclid.bbms/1323787166


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