| Title:
|
On the structure of the solution set of a functional-differential system on an unbounded interval (English) |
| Author:
|
Kubáček, Zbyněk |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
35 |
| Issue:
|
3 |
| Year:
|
1999 |
| Pages:
|
215-228 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that under some conditions the set of all solutions of an initial value problem for $n$-th order functional differential system on an unbounded interval is a compact $R_\delta $. (English) |
| Keyword:
|
initial value problem |
| Keyword:
|
functional differential system |
| Keyword:
|
$R_\delta$-set |
| MSC:
|
34K05 |
| MSC:
|
34K12 |
| MSC:
|
47H10 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1054.34103 |
| idMR:
|
MR1725839 |
| . |
| Date available:
|
2008-06-06T22:23:14Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107697 |
| . |
| Reference:
|
[1] Andres J., Gabor G., Górniewicz L.: Boundary value problems on infinite intervals.Trans. Am. Math. Soc. (to appear). MR 1603870 |
| Reference:
|
[2] Andres J., Gabor G., Górniewicz L.: Topological structure of solution sets to multivalued asymptotic problems.Přírodovědecká fakulta UP Olomouc, Katedra mat. analýzy a aplikací matematiky, Preprint 1, 1999. MR 1603870 |
| Reference:
|
[3] Aubin J. P., Cellina A.: Differential Inclusions, Set-Valued Maps and Viability Theory.Berlin, Springer-Verlag 1984. Zbl 0538.34007, MR 0755330 |
| Reference:
|
[4] Kubáček Z.: On the structure of the fixed point sets of some compact maps in the Fréchet space.Mathematica Bohemica, 118 (1993), No. 4, 343–358. MR 1251881 |
| Reference:
|
[5] Šeda V., Belohorec Š.: A remark on second order functional differential systems.Archivum Mathematicum (Brno), 29 (1993), No. 3-4, 169–176. Zbl 0804.34060, MR 1263119 |
| Reference:
|
[6] Šeda V., Eliaš J.: On the initial value problem for functional differential systems.Proc. of the Georgian Acad. of Sciences, Mathematics 1 (1993), No. 4, 467–476. Zbl 0801.34062, MR 1262578 |
| Reference:
|
[7] Šeda V., Kubáček Z.: On the connectedness of the set of fixed points of a compact operator in the Fréchet space $C^m([b,\infty ),\text{R}^n)$.Czech. Math. J., 42(117) (1992), 577–588. MR 1182189 |
| Reference:
|
[8] Vidossich G.: A fixed point theorem for function spaces.J. Math. Anal. Appl. 36 (1971), 581–587. Zbl 0194.44903, MR 0285945 |
| . |
