| Title:
|
An existence theorem for a class of nonlinear elliptic optimal control problems (English) |
| Author:
|
Papageorgiou, Nikolaos S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
2 |
| Year:
|
1991 |
| Pages:
|
273-279 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We establish the existence of an optimal ``state-control'' pair for an optimal control problem of Lagrange type, monitored by a nonlinear elliptic partial equation involving nonmonotone nonlinearities. (English) |
| Keyword:
|
Sobolev embedding theorem |
| Keyword:
|
Novikov's theorem |
| Keyword:
|
Aumann's theorem |
| Keyword:
|
pseudomonotone operator |
| Keyword:
|
property ($M$) |
| Keyword:
|
nonlinear elliptic equation |
| MSC:
|
35B37 |
| MSC:
|
35J65 |
| MSC:
|
49A29 |
| MSC:
|
49J20 |
| MSC:
|
49J40 |
| idZBL:
|
Zbl 0752.49005 |
| idMR:
|
MR1137788 |
| . |
| Date available:
|
2009-01-08T17:43:59Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116984 |
| . |
| Reference:
|
[1] Barbu V.: Optimal Control of Variational Inequalities.Research Notes in Math., vol. 100, Pitman, Boston, 1984. Zbl 0696.49021, MR 0742624 |
| Reference:
|
[2] Browder F.: Pseudomonotone operators and nonlinear elliptic boundary value problems on unbounded domains.Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 2659-2661. MR 0445124 |
| Reference:
|
[3] Cesari L.: Optimization-Theory and Applications.Springer-Verlag, New York, 1983. Zbl 0506.49001, MR 0688142 |
| Reference:
|
[4] Delahaye J.-P., Denel J.: The continuities of the point to set maps: Definitions and equivalences.Math. Programming Study 10 (1979), 8-12. |
| Reference:
|
[5] Levin V.: Borel sections of many-valued maps.Siberian Math. Journal 19 (1978), 434-438. MR 0501769 |
| Reference:
|
[6] Lions J.-L.: Optimal Control of Systems Governed by Partial Differential Equations.SpringerVerlag, New York, 1971. Zbl 0203.09001, MR 0271512 |
| Reference:
|
[7] Raitum U.E.: On optimal control problems for linear elliptic equations.Soviet. Math. Doklady 20 (1979), 129-132. MR 0520593 |
| Reference:
|
[8] Saint-Beuve M.-F.: On the extension of von Neumann-Aumann's theorem.Journ. Funct. Analysis 17 (1974), 112-129. MR 0374364 |
| Reference:
|
[9] Zeidler E.: Nonlinear Functional Analysis and Applications II.Springer-Verlag, Berlin, 1990. |
| Reference:
|
[10] Zolezzi T.: Teoremi di esistenza per problemi di controllo ottimo retti da equazioni ellitiche o paraboliche.Rend. Sem. Mat. Univ. Padova 44 (1970), 155-173. MR 0308891 |
| . |
