| Autor: |
Eugen Stumpf |
| Jazyk: |
angličtina |
| Rok vydání: |
2015 |
| Předmět: |
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| Zdroj: |
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2015, Iss 4, Pp 1-45 (2015) |
| Druh dokumentu: |
article |
| ISSN: |
1417-3875 |
| DOI: |
10.14232/ejqtde.2015.1.4 |
| Popis: |
In the present paper we consider local center-unstable manifolds at a stationary point for a class of functional differential equations of the form $\dot{x}(t)=f(x_{t})$ under assumptions that are designed for application to differential equations with state-dependent delay. Here, we show an attraction property of these manifolds. More precisely, we prove that, after fixing some local center-unstable manifold $W_{cu}$ of $\dot{x}(t)=f(x_{t})$ at some stationary point $\varphi$, each solution of $\dot{x}(t)=f(x_{t})$ which exists and remains sufficiently close to $\varphi$ for all $t\geq 0$ and which does not belong to $W_{cu}$ converges exponentially for $t\to\infty$ to a solution on $W_{cu}$. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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