The periodic problem for semilinear differential inclusions in Banach spaces

Ralf Bader

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 4, page 671-684
  • ISSN: 0010-2628

Abstract

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Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness.

How to cite

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Bader, Ralf. "The periodic problem for semilinear differential inclusions in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 39.4 (1998): 671-684. <http://eudml.org/doc/248250>.

@article{Bader1998,
abstract = {Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness.},
author = {Bader, Ralf},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {periodic solutions; translation operator along trajectories; set-valued maps; $C_0$-semigroup; $R_\delta $-sets; periodic solutions; Poincaré operator; set-valued maps; fixed-point index},
language = {eng},
number = {4},
pages = {671-684},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The periodic problem for semilinear differential inclusions in Banach spaces},
url = {http://eudml.org/doc/248250},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Bader, Ralf
TI - The periodic problem for semilinear differential inclusions in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 4
SP - 671
EP - 684
AB - Sufficient conditions on the existence of periodic solutions for semilinear differential inclusions are given in general Banach space. In our approach we apply the technique of the translation operator along trajectories. Due to recent results it is possible to show that this operator is a so-called decomposable map and thus admissible for certain fixed point index theories for set-valued maps. Compactness conditions are formulated in terms of the Hausdorff measure of noncompactness.
LA - eng
KW - periodic solutions; translation operator along trajectories; set-valued maps; $C_0$-semigroup; $R_\delta $-sets; periodic solutions; Poincaré operator; set-valued maps; fixed-point index
UR - http://eudml.org/doc/248250
ER -

References

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  2. Bader R., Fixpunktindextheorie mengenwertiger Abbildungen und einige Anwendungen, Ph.D. Dissertation, Universität München, 1995. Zbl0865.47049
  3. Bader R., Fixed point theorems for compositions of set-valued maps with single-valued maps, submitted. Zbl1012.47043
  4. Bader R., Kryszewski W., Fixed-point index for compositions of set-valued maps with proximally ∞ -connected values on arbitrary ANR’s, Set-Valued Analysis 2 (1994), 459-480. (1994) Zbl0846.55001MR1304049
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