| Autor: |
Bernhard Lani-Wayda, Jaqueline Godoy Mesquita |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2023, Iss 52, Pp 1-52 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
1417-3875 |
| DOI: |
10.14232/ejqtde.2023.1.52 |
| Popis: |
We provide a criterion for instability of equilibria of equations in the form $\dot x(t) = g(x_t', x_t)$, which includes neutral delay equations with state-dependent delay. The criterion is based on a lower bound $\Delta >0$ for the delay in the neutral terms, on regularity assumptions of the functions in the equation, and on spectral assumptions on a semigroup used for approximation. The spectral conditions can be verified studying the associated characteristic equation. Estimates in the $C^1$-norm, a manifold containing the state space $X_2$ of the equation and another manifold contained in $X_2$, and an invariant cone method are used for the proof. We also give mostly self-contained proofs for the necessary prerequisites from the constant delay case, and conclude with an application to a mechanical example. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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