A new theorem on exponential stability of periodic evolution families on Banach spaces
| dc.contributor.author | Buse, Constantin | |
| dc.contributor.author | Jitianu, Oprea | |
| dc.date.accessioned | 2020-09-14T19:20:15Z | |
| dc.date.available | 2020-09-14T19:20:15Z | |
| dc.date.issued | 2003-02-11 | |
| dc.description.abstract | We consider a mild solution v<sub>f</sub> (·, 0) of a well-posed inhomogeneous Cauchy problem v̇(t) = A(t)v(t) + ƒ(t), v(0) = 0 on a complex Banach space X, where A(·) is a 1-periodic operator-valued function. We prove that if vƒ (·, 0) belongs to AP0 (ℝ₊, X) for each ƒ ∈ AP0(ℝ₊, X) then for each x ∈ X the solution of the well-posed Cauchy problem u̇(t) = A(t)v(t), u(0) = x is uniformly exponentially stable. The converse statement is also true. Details about the space AP0(ℝ₊, X) are given in the section 1, below. Our approach is based on the spectral theory of evolution semigroups. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Buse, C., & Jitianu, O. (2003). A new theorem on exponential stability of periodic evolution families on Banach spaces. <i>Electronic Journal of Differential Equations, 2003</i>(14), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12605 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Almost periodic functions | |
| dc.subject | Exponential stability | |
| dc.subject | Periodic evolution families of operators | |
| dc.subject | Integral inequality | |
| dc.subject | Differential inequality on Banach spaces | |
| dc.title | A new theorem on exponential stability of periodic evolution families on Banach spaces | |
| dc.type | Article |