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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Uniform asymptotic stability via Liapunov-Razumikhin technique


Author: James H. Liu
Journal: Proc. Amer. Math. Soc. 123 (1995), 2465-2471
MSC: Primary 45J05; Secondary 34K20, 45M10
MathSciNet review: 1257116
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Abstract: The Liapunov-Razumikhin technique is applied to obtain the uniform asymptotic stability for linear integrodifferential equations in Hilbert spaces,

$\displaystyle x'(t) = A\left[ {x(t) + \int_\char93 ^t {F(t - s)x(s)\,ds} } \right],\quad t \geq {t_0} \geq 0(\char93 = 0\;{\text{or}} - \infty ),$

which occur in viscoelasticity and in heat conduction for materials with memory.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1257116-8
PII: S 0002-9939(1995)1257116-8
Keywords: Uniform asymptotic stability, Liapunov-Razumikhin technique
Article copyright: © Copyright 1995 American Mathematical Society