Geodesic
On the structure of the solution set of a functional-differential system on an unbounded interval
Archivum mathematicum, Tome 35 (1999) no. 3, pp. 215-228 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $.
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 $.
Classification : 34K05, 34K12, 47H10, 47N20
Keywords: initial value problem; functional differential system; $R_\delta$-set 
@article{ARM_1999_35_3_a2,
     author = {Kub\'a\v{c}ek, Zbyn\v{e}k},
     title = {On the structure of the solution set of a functional-differential system on an unbounded interval},
     journal = {Archivum mathematicum},
     pages = {215--228},
     year = {1999},
     volume = {35},
     number = {3},
     mrnumber = {1725839},
     zbl = {1054.34103},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1999_35_3_a2/}
}
TY  - JOUR
AU  - Kubáček, Zbyněk
TI  - On the structure of the solution set of a functional-differential system on an unbounded interval
JO  - Archivum mathematicum
PY  - 1999
SP  - 215
EP  - 228
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ARM_1999_35_3_a2/
LA  - en
ID  - ARM_1999_35_3_a2
ER  - 
%0 Journal Article
%A Kubáček, Zbyněk
%T On the structure of the solution set of a functional-differential system on an unbounded interval
%J Archivum mathematicum
%D 1999
%P 215-228
%V 35
%N 3
%U http://geodesic.mathdoc.fr/item/ARM_1999_35_3_a2/
%G en
%F ARM_1999_35_3_a2
Kubáček, Zbyněk. On the structure of the solution set of a functional-differential system on an unbounded interval. Archivum mathematicum, Tome 35 (1999) no. 3, pp. 215-228. http://geodesic.mathdoc.fr/item/ARM_1999_35_3_a2/

[1] Andres J., Gabor G., Górniewicz L.: Boundary value problems on infinite intervals. Trans. Am. Math. Soc. (to appear). | MR

[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

[3] Aubin J. P., Cellina A.: Differential Inclusions, Set-Valued Maps and Viability Theory. Berlin, Springer-Verlag 1984. | MR | Zbl

[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

[5] Šeda V., Belohorec Š.: A remark on second order functional differential systems. Archivum Mathematicum (Brno), 29 (1993), No. 3-4, 169–176. | MR | Zbl

[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. | MR | Zbl

[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

[8] Vidossich G.: A fixed point theorem for function spaces. J. Math. Anal. Appl. 36 (1971), 581–587. | MR | Zbl