Massera Type Theorem for Abstract Functional Differential Equations
| dc.creator | Liu, Qing | |
| dc.creator | Van Minh, Nguyen | |
| dc.creator | Nguerekata, G. | |
| dc.creator | Yuan, Rong | |
| dc.date | 2006-12-07 | |
| dc.date | 2007-09-20 | |
| dc.date.accessioned | 2026-07-07T08:30:56Z | |
| dc.date.available | 2026-07-07T08:30:56Z | |
| dc.description | The paper is concerned with conditions for the existence of almost periodic solutions of the following abstract functional differential equation $ \dot u(t) = Au(t) + [{\cal B}u](t) +f(t), $ where $A$ is a closed operator in a Banach space $\X$, $\cal B$ is a general bounded linear operator in the function space of all $\X$-valued bounded and uniformly continuous functions that satisfies a so-called {\it autonomous} condition. We develop a general procedure to carry out the decomposition that does not need the well-posedness of the equations. The obtained conditions are of Massera type, which are stated in terms of spectral conditions of the operator ${\cal A}+{\cal B}$ and the spectrum of $f$. Moreover, we give conditions for the equation not to have quasi-periodic solutions with different structures of spectrum. The obtained results extend previous ones. | |
| dc.description | 18 pages | |
| dc.identifier | https://arxiv.org/abs/math/0612197 | |
| dc.identifier | http://arxiv.org/abs/math/0612197 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138373 | |
| dc.subject | Functional Analysis | |
| dc.subject | Dynamical Systems | |
| dc.subject | 47D06, 34C27 | |
| dc.title | Massera Type Theorem for Abstract Functional Differential Equations | |
| dc.type | text |