Linearized instability for differential equations with dependence on the past derivative
We provide a criterion for instability of equilibria of equations in the form x˙(t) = g(x t , xt), which includes neutral delay equations with state-dependent delay. The criterion is based on a lower bound ∆ > 0 for the delay in the neutral terms, on regularity assumptions of the functions in the...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2023
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet - késleltetett, Differenciálegyenlet - funkcionális |
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| doi: | 10.14232/ejqtde.2023.1.52 |
| Online Access: | http://acta.bibl.u-szeged.hu/88795 |
| Tartalmi kivonat: | We provide a criterion for instability of equilibria of equations in the form x˙(t) = g(x t , xt), which includes neutral delay equations with state-dependent delay. The criterion is based on a lower bound ∆ > 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 X2 of the equation and another manifold contained in X2, 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. |
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| Terjedelem/Fizikai jellemzők: | 52 |
| ISSN: | 1417-3875 |