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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| _version_ | 1832545356031721472 |
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| author | Jin Liang Falun Huang Tijun Xiao |
| author_facet | Jin Liang Falun Huang Tijun Xiao |
| author_sort | Jin Liang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2a5dca8d7d624823b805acd5443a6280 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2a5dca8d7d624823b805acd5443a62802025-02-03T07:25:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121225525910.1155/S0161171298000362Exponential stability for abstract linear autonomous functional differential equations with infinite delayJin Liang0Falun Huang1Tijun Xiao2Teaching and Research Section of Mathematics, Kunming University of Science and Technology, Kunming 650093, ChinaDepartment of Mathematics, Sichuan University, Chengdu 610064, ChinaDepartment of Mathematics, Yunnan Normal University, Kunming 650092, ChinaBased 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.http://dx.doi.org/10.1155/S0161171298000362Exponentially stablesolution semigroupabstract linear autonomous functional differential equationfundamental operatorfading memory space. |
| spellingShingle | Jin Liang Falun Huang Tijun Xiao Exponential stability for abstract linear autonomous functional differential equations with infinite delay International Journal of Mathematics and Mathematical Sciences Exponentially stable solution semigroup abstract linear autonomous functional differential equation fundamental operator fading memory space. |
| title | Exponential stability for abstract linear autonomous functional differential equations with infinite delay |
| title_full | Exponential stability for abstract linear autonomous functional differential equations with infinite delay |
| title_fullStr | Exponential stability for abstract linear autonomous functional differential equations with infinite delay |
| title_full_unstemmed | Exponential stability for abstract linear autonomous functional differential equations with infinite delay |
| title_short | Exponential stability for abstract linear autonomous functional differential equations with infinite delay |
| title_sort | exponential stability for abstract linear autonomous functional differential equations with infinite delay |
| topic | Exponentially stable solution semigroup abstract linear autonomous functional differential equation fundamental operator fading memory space. |
| url | http://dx.doi.org/10.1155/S0161171298000362 |
| work_keys_str_mv | AT jinliang exponentialstabilityforabstractlinearautonomousfunctionaldifferentialequationswithinfinitedelay AT falunhuang exponentialstabilityforabstractlinearautonomousfunctionaldifferentialequationswithinfinitedelay AT tijunxiao exponentialstabilityforabstractlinearautonomousfunctionaldifferentialequationswithinfinitedelay |