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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| _version_ | 1832563080817541120 |
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| author | Jin Liang Tijun Xiao |
| author_facet | Jin Liang Tijun Xiao |
| author_sort | Jin Liang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5bb8ea6b4ca348d498f320b2fd330ea7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5bb8ea6b4ca348d498f320b2fd330ea72025-02-03T01:20:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114349750810.1155/S0161171291000686Functional differential equations with infinite delay in Banach spacesJin Liang0Tijun Xiao1Teaching and Research Section of Mathematics, Kunming Engineering Institute, Kunming, ChinaDepartment of Mathematics, Yunnan Teachers' University, Kunming, ChinaIn 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.http://dx.doi.org/10.1155/S0161171291000686functional differential equation with infinite delayBanach space fundamental operatorexponentially stablephase space. |
| spellingShingle | Jin Liang Tijun Xiao Functional differential equations with infinite delay in Banach spaces International Journal of Mathematics and Mathematical Sciences functional differential equation with infinite delay Banach space fundamental operator exponentially stable phase space. |
| title | Functional differential equations with infinite delay in Banach spaces |
| title_full | Functional differential equations with infinite delay in Banach spaces |
| title_fullStr | Functional differential equations with infinite delay in Banach spaces |
| title_full_unstemmed | Functional differential equations with infinite delay in Banach spaces |
| title_short | Functional differential equations with infinite delay in Banach spaces |
| title_sort | functional differential equations with infinite delay in banach spaces |
| topic | functional differential equation with infinite delay Banach space fundamental operator exponentially stable phase space. |
| url | http://dx.doi.org/10.1155/S0161171291000686 |
| work_keys_str_mv | AT jinliang functionaldifferentialequationswithinfinitedelayinbanachspaces AT tijunxiao functionaldifferentialequationswithinfinitedelayinbanachspaces |