Abstract
In this paper, controllability for the system originating from semilinear functional differential equations in Hilbert spaces is studied. We consider the problem of approximate controllability of semilinear differential inclusion assuming that semigroup, generated by the linear part of the inclusion, is compact and under the assumption that the corresponding linear system is approximately controllable. By using resolvent of controllability Gramian operator and fixed point theorem, sufficient conditions have been formulated and proved. An example is presented to illustrate the utility and applicability of the proposed method.
| Original language | English |
|---|---|
| Pages (from-to) | 2701-2712 |
| Number of pages | 12 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 75 |
| Issue number | 5 |
| DOIs | |
| State | Published - Mar 2012 |
| Externally published | Yes |
Funding
This work was supported in part by the Marshall of Kuyavian–Pomeranian Voivodeship (Województwo Kujawsko–Pomorskie) in Poland with the funds from European Social Fund (EFS) (a part of integrated operational program for regional development, activity 2.6—“w ramach Zintegrowanego Programu Rozwoju Regionalnego ZPORR, działanie 2.6”) in the form of a grant for Ph.D. students (step in the future program, second edition—“Krok w przyszłość stypendia dla doktorantów druga edycja”).
| Funders | Funder number |
|---|---|
| Marshall of Kuyavian | |
| European Social Fund | |
| Etablissement français du sang |
Keywords
- Approximate controllability
- Fixed point
- Hilbert space
- Mild solution
- Multivalued map
- Semilinear differential inclusion