Exponential stability for abstract linear autonomous functional differential equations with infinite delay
Based on our preceding paper, this note is concerned with the exponential stability of the solution semigroup for the abstract linear autonomous functional differential equation x˙(t)=L(xt) (∗) where L is a continuous linear operator on some abstract phase space B into...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000362 |
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| Summary: | Based on our preceding paper, this note is concerned with the exponential stability of the
solution semigroup for the abstract linear autonomous functional differential equation
x˙(t)=L(xt) (∗)
where L is a continuous linear operator on some abstract phase space B
into a Banach space E. We
prove that the solution semigroup of (∗) is exponentially stable if and only if the fundamental operator (∗)
is exponentially stable and the phase space B
is an exponentially fading memory space. |
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| ISSN: | 0161-1712 1687-0425 |