Eigenvalue theorems for compact and condensing set-valued maps in topological vector spaces

Siegfried Hahn

Commentationes Mathematicae Universitatis Carolinae (1979)

  • Volume: 020, Issue: 1, page 123-141
  • ISSN: 0010-2628

How to cite

top

Hahn, Siegfried. "Eigenwertaussagen für kompakte und kondensierende mengenwertige Abbildungen in topologischen Vektorräumen." Commentationes Mathematicae Universitatis Carolinae 020.1 (1979): 123-141. <http://eudml.org/doc/16952>.

@article{Hahn1979,
author = {Hahn, Siegfried},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {measure of noncompactness; condensing map; compact map; nonlinear eigenvalue problem},
language = {ger},
number = {1},
pages = {123-141},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Eigenwertaussagen für kompakte und kondensierende mengenwertige Abbildungen in topologischen Vektorräumen},
url = {http://eudml.org/doc/16952},
volume = {020},
year = {1979},
}

TY - JOUR
AU - Hahn, Siegfried
TI - Eigenwertaussagen für kompakte und kondensierende mengenwertige Abbildungen in topologischen Vektorräumen
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1979
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 020
IS - 1
SP - 123
EP - 141
LA - ger
KW - measure of noncompactness; condensing map; compact map; nonlinear eigenvalue problem
UR - http://eudml.org/doc/16952
ER -

References

top
  1. G. D. BIRKHOFF O. D. KELLOGG, Invariant points in function spaces, Transact. Amer. Math. Soc. 23, 96-115 (1922). (1922) MR1501192
  2. K. FAN, Fixed point and minimax theorems in locally convex linear spaces, Proc. Nat. Acad. Sci. USA 38, 121-126 (1952). (1952) MR0047317
  3. P. M. FITZPATRICK W. V. PETRYSHYN, Fixed point theorems and the fixed point index for mappings in cones, J. London Math. Soc. (2), 11, 75-85 (1975). (1975) MR0405180
  4. P. M. FITZPATRICK W. V. PETRYSHYN, Positive eigenvalues for nonlinear multivalued noncompact operators with applications to Differential operators, Journ. Differential Equ. 22, 428-441 (1976). (1976) MR0435958
  5. A. GRANAS, The theory of compact vector fields and some of its applications to topology of functional spaces (I), Rozprawy Mat. 30, Warszawa 1962. (1962) MR0149253
  6. S. HAHN, Zur Leray-Schauder-Theorie in topologischen Vektorräumen, Wiss. Zeitschr. Techn. Univ. Dresden 24, 375-378 (1975). (1975) Zbl0317.47036MR0438195
  7. S. HAHN, Fixpunktsätze für mengenwertife Abbildungen in lokalkonvexen Räumen, Math. Nachr. 73, 269-283 (1976). (1976) MR0433269
  8. S. HAHN, Gebietsinvarianzsatz und Eigenwertaussafen für konzentrierende Abbildungen, Comment. Math. Univ. Carolinae 18, 697-713 (1977). (1977) MR0474385
  9. S. HAHN, Ein Homotopieerweiterungssatz für konzentrierende Abbildungen in lokalkonvexen Räumen, eгcheint im Studia Math. 66, 2. MR0565153
  10. S. HAHN, A remark on a fixed point theorem for condensing set-valued mappings, Preprint TU Dresden 1977, 77/07/05. (1977) 
  11. G. KAYSER, Zuг Existenz von Fixpunkten bei kompaktem bzw. konzentrierenden mengenwertigen Abbildungen in lokalkonvexen Räumen, Berichte der Jahrestagung Num. Math. Potsdam-Cecilienhof, 25. 11. - 1. 12. 1973, 46-53, T. N. Karl-Marx-Stadt, Sektion Mathematik. (1973) 
  12. M. A. KRASNOSELSKI, Positive Lösungen von Operatorengleichungen, (russ.), Moskau 1962. (1962) 
  13. M. LANDSBERG T. RIEDRICH, Über positive Eigenwerte kompakter Abbildungen in topologischen Vektorräumen, Math. Ann. 163, 50-61 (1966). (1966) MR0196546
  14. T. W. MA, Topological degrees of set-valued compact fields in locally convex spaces, Diss. Math. 92 (1972). (1972) Zbl0211.25903MR0309103
  15. M. MARTELLI, A Rothe's type theorem for noncompact acyclic-valued maps, Proceedings of the conference on problems in nonlinear functional analysis, Universitat Bonn July 22-26, 1975. Ber. Ges. f. Math. u. Datenverarbeitung Bonn, Nr. 103 (1975). (1975) Zbl0333.47025MR0435952
  16. R. D. NUSSBAUM, Some fixed point theorems, Bull. Amer. Math. Soc. 77, 360-365 (1971). (1971) Zbl0212.16502MR0284888
  17. S. REICH, Characteristic vectors of nonlinear operators, Rend. Accad. Naz. Lincei 50, 682-685 (1971). (1971) Zbl0231.47042MR0306987
  18. T. RIEDRICH, Das Birkhoff-Kellog-Theorem für lokal radial beschränkte Räume, Math. Ann. 166, 264-276 (1966). (1966) MR0203536
  19. T. RIEDRICH, Verlösungen über nichtlineare Operaterengleichungen, Teubner-Texte, Leipzig 1976. (1976) MR0467414
  20. B. N. SADOWSKI, Limeskompakte und kondensierende Abbildungen, Uspechi mat. nauk, 27, 1, 81-146 (1972) (гuss.). (1972) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.