Buică, Adriana (2023) Ulam–Hyers stability and exponentially dichotomic equations in Banach spaces. ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2023 (8). pp. 1-10. ISSN 1417-3875
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Official URL: https://doi.org/10.14232/ejqtde.2023.1.8
Abstract
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 Rwith uniqueness. We also consider abstract non-autonomous evolution equations which are exponentially bounded and exponentially dichotomic and prove that UlamHyers stability with uniqueness is maintained when perturbing them with a nonlinear term having a sufficiently small Lipschitz constant.
| Item Type: | Article |
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| Uncontrolled Keywords: | Ulam–Hyers stability, evolution family, nonautonomous, mild solution, exponential dichotomy, small Lipschitz constant |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| Depositing User: | Kotegelt Import |
| Date Deposited: | 18 Jan 2024 09:44 |
| Last Modified: | 28 Mar 2024 13:03 |
| URI: | https://real.mtak.hu/id/eprint/185158 |
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