Functional differential equations with infinite delay in Banach spaces
In this paper, a definition of the fundamental operator for the linear autonomous functional differential equation with infinite delay in a Banach space is given, and some sufficient and necessary conditions of the fundamental operator being exponentially stable in abstract phase spaces which satisf...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000686 |
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| Summary: | In this paper, a definition of the fundamental operator for the linear autonomous functional
differential equation with infinite delay in a Banach space is given, and some sufficient and necessary
conditions of the fundamental operator being exponentially stable in abstract phase spaces which satisfy
some suitable hypotheses are obtained. Moreover, we discuss the relation between the exponential
asymptotic stability of the zero solution of nonlinear functional differential equation with infinite delay in
a Banach space and the exponential stability of the solution semigroup of the corresponding linear equation,
and find that the exponential stability problem of the zero solution for the nonlinear equation can be discussed
only in the exponentially fading memory phase space. |
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| ISSN: | 0161-1712 1687-0425 |