Ulam-Hyers stability and exponentially dichotomic evolution equations in Banach spaces
For finite-dimensional linear differential systems with bounded coefficients we prove that their exponential dichotomy on R is equivalent to their Ulam–Hyers stability on R with uniqueness. We also consider abstract non-autonomous evolution equations which are exponentially bounded and exponentially...
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: | Banach tér, Evolúciós egyenlet |
| doi: | 10.14232/ejqtde.2023.1.8 |
| Online Access: | http://acta.bibl.u-szeged.hu/82258 |
| Tartalmi kivonat: | For finite-dimensional linear differential systems with bounded coefficients we prove that their exponential dichotomy on R is equivalent to their Ulam–Hyers stability on R with uniqueness. We also consider abstract non-autonomous evolution equations which are exponentially bounded and exponentially dichotomic and prove that Ulam– Hyers stability with uniqueness is maintained when perturbing them with a nonlinear term having a sufficiently small Lipschitz constant. |
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| Terjedelem/Fizikai jellemzők: | 10 |
| ISSN: | 1417-3875 |