# Article

Full entry | PDF   (0.3 MB)
Keywords:
initial value problem; functional differential system; $R_\delta$-set
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 $R_\delta$.
References:
[1] Andres J., Gabor G., Górniewicz L.: Boundary value problems on infinite intervals. Trans. Am. Math. Soc. (to appear). MR 1603870
[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
[3] Aubin J. P., Cellina A.: Differential Inclusions, Set-Valued Maps and Viability Theory. Berlin, Springer-Verlag 1984. MR 0755330 | Zbl 0538.34007
[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
[5] Šeda V., Belohorec Š.: A remark on second order functional differential systems. Archivum Mathematicum (Brno), 29 (1993), No. 3-4, 169–176. MR 1263119 | Zbl 0804.34060
[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 1262578 | Zbl 0801.34062
[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
[8] Vidossich G.: A fixed point theorem for function spaces. J. Math. Anal. Appl. 36 (1971), 581–587. MR 0285945 | Zbl 0194.44903

Partner of