| Title:
|
Extremal solutions and relaxation for second order vector differential inclusions (English) |
| Author:
|
Avgerinos, Evgenios P. |
| Author:
|
Papageorgiou, Nikolaos S. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
34 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
427-434 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider periodic and Dirichlet problems for second order vector differential inclusions. First we show the existence of extremal solutions of the periodic problem (i.e. solutions moving through the extreme points of the multifunction). Then for the Dirichlet problem we show that the extremal solutions are dense in the $C^1(T,R^N)$-norm in the set of solutions of the “convex” problem (relaxation theorem). (English) |
| Keyword:
|
lower semicontinuous multifunctions |
| Keyword:
|
continuous embedding |
| Keyword:
|
compact embedding |
| Keyword:
|
continuous selector |
| Keyword:
|
extremal solution |
| Keyword:
|
relaxation theorem |
| MSC:
|
34A60 |
| MSC:
|
34B15 |
| MSC:
|
34C25 |
| idZBL:
|
Zbl 0973.34010 |
| idMR:
|
MR1679637 |
| . |
| Date available:
|
2009-02-17T10:15:44Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107670 |
| . |
| Reference:
|
[1] Benamara M.: Points extremaux, multiapplications et fonctionelles integrales.These de 3eme cycle, Universite de Grenoble 1975. |
| Reference:
|
[2] Bressan A., Colombo G.: Extensions and selections on maps with decomposable values.Studia Math., XC(1988), 69-85. MR 0947921 |
| Reference:
|
[3] Brezis H.: Analyse Fonctionelle.Masson, Paris (1983). MR 0697382 |
| Reference:
|
[4] Frigon M.: Problemes aux limites pour des inclusions differentilles de type semi-continues inferieument.Rivista Math. Univ. Parma 17(1991), 87-97. MR 1174938 |
| Reference:
|
[5] Gutman S.: Topological equivalence in the space of integrable vector valued functions.Proc. AMS. 93(1985), 40-42. Zbl 0529.46027, MR 0766523 |
| Reference:
|
[6] Kisielewicz M.: Differential Inclusions and Optimal Control.Kluwer, Dordrecht, The Netherlands, (1991). MR 1135796 |
| Reference:
|
[7] Klein E., Thompson A.: Theory of Correspondences.Wiley, New York, (1984). Zbl 0556.28012, MR 0752692 |
| Reference:
|
[8] Papageorgiou N. S.: On measurable multifunctions with applications to random multivalued equations.Math. Japonica, 32, (1987), 437-464. Zbl 0634.28005, MR 0914749 |
| Reference:
|
[9] Šeda V.: On some nonlinear boundary value problems for ordinary differential equations.Archivum Math. (Brno) 25(1989), 207-222. MR 1188065 |
| Reference:
|
[10] Tolstonogov A. A.: Extreme continuous selectors for multivalued maps and the bang-bang principle for evolution equations.Soviet. Math. Doklady 42(1991), 481-485. MR 1121349 |
| Reference:
|
[11] Wagner D.: Surveys of measurable selection theorems.SIAM J. Control Optim. 15 (1977), 857-903. MR 0486391 |
| . |
