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Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations
Joint Authors
Moşincat, Răzvan O.
Preda, Ciprian
Preda, Petre
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-23, 23 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-01-23
Country of Publication
Egypt
No. of Pages
23
Main Subjects
Abstract EN
We analyze the existence of (no past) exponential dichotomies for a well-posed autonomous differential equation (that generates a C 0-semigroup { T ( t ) } t ≥ 0 ).
The novelty of our approach consists in the fact that we do not assume the T(t)-invariance of the unstable manifolds.
Roughly speaking, we prove that if the solution of the corresponding inhomogeneous difference equation belongs to any sequence space (on which the right shift is an isometry) for every inhomogeneity from the same class of sequence spaces, then the continuous-time solutions of the autonomous homogeneous differential equation will exhibit a (no past) exponential dichotomic behavior.
This approach has many advantages among which we emphasize on the facts that the aforementioned condition is very general (since the class of sequence spaces that we use includes almost all the known sequence spaces, as the classical ℓ p spaces, sequence Orlicz spaces, etc.) and that from discrete-time conditions we get information about the continuous-time behavior of the solutions.
American Psychological Association (APA)
Moşincat, Răzvan O.& Preda, Ciprian& Preda, Petre. 2012. Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations. Journal of Function Spaces،Vol. 2012, no. 2012, pp.1-23.
https://search.emarefa.net/detail/BIM-994231
Modern Language Association (MLA)
Moşincat, Răzvan O.…[et al.]. Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations. Journal of Function Spaces No. 2012 (2012), pp.1-23.
https://search.emarefa.net/detail/BIM-994231
American Medical Association (AMA)
Moşincat, Răzvan O.& Preda, Ciprian& Preda, Petre. Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations. Journal of Function Spaces. 2012. Vol. 2012, no. 2012, pp.1-23.
https://search.emarefa.net/detail/BIM-994231
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-994231