Parameter Dependence of Stable Invariant Manifolds for Delay Differential Equations under (μ,ν)-Dichotomies
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-10-27
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We obtain the existence of stable invariant manifolds for the nonlinear equation x′=L(t)xt+f(t,xt,λ) provided that the linear delay equation x′=L(t)xt admits a nonuniform (μ,ν)-dichotomy and f is a sufficiently small Lipschitz perturbation.
We show that the stable invariant manifolds are dependent on parameter λ.
Namely, the stable invariant manifolds are Lipschitz in the parameter λ.
In addition, we also show that nonuniform (μ,ν)-contraction persists under sufficiently small nonlinear perturbations.
American Psychological Association (APA)
Pan, Lijun. 2014. Parameter Dependence of Stable Invariant Manifolds for Delay Differential Equations under (μ,ν)-Dichotomies. Journal of Mathematics،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1041116
Modern Language Association (MLA)
Pan, Lijun. Parameter Dependence of Stable Invariant Manifolds for Delay Differential Equations under (μ,ν)-Dichotomies. Journal of Mathematics No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-1041116
American Medical Association (AMA)
Pan, Lijun. Parameter Dependence of Stable Invariant Manifolds for Delay Differential Equations under (μ,ν)-Dichotomies. Journal of Mathematics. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1041116
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1041116