Skip to main content
SpringerLink
Log in

Ein Existenz- und Eindeutigkeitssatz für die Hammersteinsche Gleichung in Banachräumen

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literatur

  1. Agmon, S.: Lectures on elliptic boundary value problems. Princeton, New Jersey: Van Nostrand Comp., Inc. 1965.

    Google Scholar 

  2. Amann, H.: Über die Existenz und iterative Berechnung einer Lösung der Hammerstein'schen Gleichung. Aequationes mathematicae1, 242–266 (1968).

    Google Scholar 

  3. Browder, F. E.: Problèmes non-linéaires. Les presses de l'université de Montréal, Montréal 1966

  4. —, and B. A. Ton: Nonlinear functional equations in Banach spaces and elliptic super-regularization. Math. Z.105, 177–195 (1968).

    Google Scholar 

  5. Dolph, C. L., and G. J. Minty. On nonlinear integral equations of Hammerstein type. In: P. M. Anselone, Editor, Nonlinear Integral Equatiosn, p. 99–154. Madison: The University of Wisconsin Press 1964.

    Google Scholar 

  6. Goldberg, S.: Unbounded linear operators; theory and applications. New York: McGraw-Hill Book Co. 1966.

    Google Scholar 

  7. Hammerstein, A.: Nichtlineare Integralgleichungen nebst Anwendungen. Acta Math.54, 117–176 (1930).

    Google Scholar 

  8. Heinz, E.: Beiträge zur Störungstheorie der Spektralzerlegung. Math. Ann.123, 415–438 (1951).

    Google Scholar 

  9. Hildebrandt, S.: Über den numerischen Wertebereich eines Operators. Math. Ann.163, 230–247 (1966).

    Google Scholar 

  10. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  11. Kolodner, I. I.: Equations of Hammerstein type in Helbert spaces. J. Math. Mech.13, 701–750 (1964).

    Google Scholar 

  12. Krasnosel'skii, M. A.: Topological methods in the theory of nonlinear integral equations. Oxford: Pergamon Press 1964.

    Google Scholar 

  13. —, and Ja. B. Rutickii: Orlicz spaces and nonlinear integral equations. Trudy Moskow. Mat. Obsc.7, 63–120 (1958); engl. Übers. in Amer. Math. Soc. Translations (2)60 51–115 (1967).

    Google Scholar 

  14. ——: Convex functions and Orlicz spaces. Groningen: P. Noordhoff Ltd. 1961.

    Google Scholar 

  15. Luxemburg, W. A. J., and A. C. Zaanen: Compactness of integral operators in Banach function spaces. Math. Ann.149, 150–180 (1963).

    Google Scholar 

  16. ——: Some examples of normed Köthe spaces. Math. Ann.162, 337–350 (1966).

    Google Scholar 

  17. Olagunju, P. A.: A Banach space that cannot be made into a BIP space. Proc. Cambridge Philos. Soc.63, 949–950 (1967).

    Google Scholar 

  18. Phillips, R. S.: Dissipative operators and hyperbolic systems of partial differential equations. Trans. Amer. Math. Soc.90, 193–254 (1959).

    Google Scholar 

  19. Vainberg, M. M.: Variational methods for the study of nonlinear operators. San Francisco: Holden-Day Inc. 1964.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Albert-Ludwigs-Universität, Hebelstraße 40, 78, Freiburg

    Herbert Amann

Authors
  1. Herbert Amann
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Amann, H. Ein Existenz- und Eindeutigkeitssatz für die Hammersteinsche Gleichung in Banachräumen. Math Z 111, 175–190 (1969). https://doi.org/10.1007/BF01113284

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01113284

Search

Navigation