On the structure of the solution set of a functional-differential system on an unbounded interval

Zbyněk Kubáček

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 3, page 215-228
  • ISSN: 0044-8753

Abstract

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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 δ .

How to cite

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Kubáček, Zbyněk. "On the structure of the solution set of a functional-differential system on an unbounded interval." Archivum Mathematicum 035.3 (1999): 215-228. <http://eudml.org/doc/248361>.

@article{Kubáček1999,
abstract = {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 $.},
author = {Kubáček, Zbyněk},
journal = {Archivum Mathematicum},
keywords = {initial value problem; functional differential system; $R_\delta $-set; initial value problem; functional-differential system},
language = {eng},
number = {3},
pages = {215-228},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the structure of the solution set of a functional-differential system on an unbounded interval},
url = {http://eudml.org/doc/248361},
volume = {035},
year = {1999},
}

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
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 3
SP - 215
EP - 228
AB - 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 $.
LA - eng
KW - initial value problem; functional differential system; $R_\delta $-set; initial value problem; functional-differential system
UR - http://eudml.org/doc/248361
ER -

References

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  1. Andres J., Gabor G., Górniewicz L., Boundary value problems on infinite intervals, Trans. Am. Math. Soc. (to appear). MR1603870
  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. (1999) MR1603870
  3. Aubin J. P., Cellina A., Differential Inclusions, Set-Valued Maps and Viability Theory, Berlin, Springer-Verlag 1984. (1984) Zbl0538.34007MR0755330
  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. (1993) MR1251881
  5. Šeda V., Belohorec Š., A remark on second order functional differential systems, Archivum Mathematicum (Brno), 29 (1993), No. 3-4, 169–176. (1993) Zbl0804.34060MR1263119
  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. (1993) Zbl0801.34062MR1262578
  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 , ∞ ) , R n ) , Czech. Math. J., 42(117) (1992), 577–588. (1992) MR1182189
  8. Vidossich G., A fixed point theorem for function spaces, J. Math. Anal. Appl. 36 (1971), 581–587. (1971) Zbl0194.44903MR0285945

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