Skip to main content
SpringerLink
Log in

Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem

  • Conference paper
  • First Online:
Fixed Point Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 886))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BONSALL, F.F.: Linear operators in complete positive cones, Proc. London Math. Soc. 8 (1958), 53–75.

    Article  MathSciNet  MATH  Google Scholar 

  2. BONSALL, F.F.: Positive operators compact in an auxiliary topology, Pacific J. Math. 10 (1960), 1131–1138.

    Article  MathSciNet  MATH  Google Scholar 

  3. BONSALL, F.F.: Lectures on Some Fixed Point Theorems of Functional Analysis, Tata Institute of Fundamental Research, Bombay, 1962.

    Google Scholar 

  4. BUMBY, R.T.: Hausdorff dimension of Cantor sets, to appear.

    Google Scholar 

  5. DARBO, G.: Punti uniti in transformazioni a condiminio non compatto, Rend. Sem. Mat. Univ. Padova 24 (1955), 353–367.

    MathSciNet  Google Scholar 

  6. DUGUNDJI, J.: An extension of Tietze’s theorem, Pacific J. Math. 1 (1951), 353–367.

    Article  MathSciNet  MATH  Google Scholar 

  7. EDMUNDS, D.A. and POTTER, A.J.B. and STUART, C.A.: Noncompact positive operators, Proc. Royal Soc. London A328 (1972), 67–81.

    Article  MathSciNet  MATH  Google Scholar 

  8. KRASNOSEL’SKIÎ, M.A.: Positive Solutions of Operator Equations, P. Noordhoff Ltd., Groningen, The Netherlands, 1964.

    Google Scholar 

  9. KREIN, M. G. and RUTMAN, M. A.: Linear operators leaving invariant a cone in a Banach space (Russian), Uspehi Mat. Nauk 3, No. 1, 23 (1948), 3–95. English translation, A.M.S. translation 26.

    MathSciNet  MATH  Google Scholar 

  10. KURATOWSKI, C.: Sur les espaces complets, Fund. Math. 15 (1930), 301–309.

    MATH  Google Scholar 

  11. LERAY, J.: Théorie des points fixes: indice total et nombre de Lefschetz, Bull. Soc. Math. France, 87 (1959), 221–233.

    MathSciNet  MATH  Google Scholar 

  12. LERAY, J. and SCHAUDER, J.: Topologic ct équations fonctionnelles, Ann. Sci. Ecole Norm. Sup. 51 (1934), 45–78.

    MathSciNet  MATH  Google Scholar 

  13. MASSABO, I. and STUART, C.A.: Positive eigenvectors of k-set-contractions, Nonlinear Analysis, T.M.A. 3 (1979), 35–44.

    MathSciNet  MATH  Google Scholar 

  14. NUSSBAUM, R.D.: The radius of the essential spectrum, Duke Math. J. 37 (1970), 473–478.

    Article  MathSciNet  MATH  Google Scholar 

  15. NUSSBAUM, R.D.: Some asymptotic fixed point theorems, Trans. Amer. Math. Soc. 171 (1972), 349–375.

    Article  MathSciNet  MATH  Google Scholar 

  16. NUSSBAUM, R.D.: The fixed point index for local condensing maps, Ann. Mat. Pura. Appl. 89 (1971), 217–258.

    Article  MathSciNet  MATH  Google Scholar 

  17. NUSSBAUM, R.D.: Generalizing the fixed point index, Math, Ann. 228 (1977), 259–278.

    Article  MathSciNet  MATH  Google Scholar 

  18. NUSSBAUM, R.D.: Integral equations from the theory of epidemics, p. 235–255 in Nonlinear systems and applications, edited by V. Laksmikantham, Academic Press, New York, (1977).

    Google Scholar 

  19. NUSSBAUM, R.D.: Periodic solutions of some nonlinear integral equations, p. 221–249, in Dynamical systems, Proceedings of a University of Florida International Symposium, edited by A.R. Bednarek and L. Cesari, Academic Press, New York, (1977).

    Google Scholar 

  20. RABINOWITZ, P.: Théorie du degré topologique et applications à des problèmes aux limites non linéaires, notes by H. Berestycki from a course at Université Paris VI, Spring, (1973).

    Google Scholar 

  21. SCHAEFER, H.H.: On nonlinear positive operators, Pacific J. Math. 9 (1959), 847–860.

    Article  MathSciNet  MATH  Google Scholar 

  22. SCHAEFER, H.H.: Some spectral properties of positive linear operators, Pacific J. Math. 10 (1960), 1009–1019.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematic Department, Rutgers University, 08903, New Brunswick, New Jersey

    Roger D. Nussbaum

Authors
  1. Roger D. Nussbaum
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Edward Fadell Gilles Fournier

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Nussbaum, R.D. (1981). Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem. In: Fadell, E., Fournier, G. (eds) Fixed Point Theory. Lecture Notes in Mathematics, vol 886. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092191

Download citation

  • DOI: https://doi.org/10.1007/BFb0092191

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11152-8

  • Online ISBN: 978-3-540-38600-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation