Archive for Rational Mechanics and Analysis

, Volume 55, Issue 3, pp 207–213 | Cite as

On the number of solutions of asymptotically superlinear two point boundary value problems

  • Herbert Amann


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aamann, H., On the number of solutions of nonlinear equations in ordered Banach spaces. J. Functional Anal. 11, 346–384 (1972).Google Scholar
  2. 2.
    Amann, H., Multiple positive fixed points of asymptotically linear maps. J. Functional Anal., to appear.Google Scholar
  3. 3.
    Aris, R., & I. Copelowitz, Communications on the theory of diffusion and reaction. V. Findings and conjectures concerning the multiplicity of solutions. Chem. Engin. Sci 25, 906–909 (1970).Google Scholar
  4. 4.
    Cohen, D. S., Multiple stable solutions of nonlinear boundary value problems arising in chemical reactor theory. SIAM J. Appl. Math. 20, 1–14 (1971).Google Scholar
  5. 5.
    Crandall, M. G., & P. H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues, and linearized stability. Arch. Rational Mech. Anal. 49, 161–180 (1973).Google Scholar
  6. 6.
    Gavalas, G. R., Nonlinear Differential Equations of Chemically Reacting Systems. Berlin-Heidelberg-New York: Springer 1968.Google Scholar
  7. 7.
    Joseph, D. D., & T. S. Lundgren, Quasilinear Dirichlet problems driven by positive sources. Arch. Rational Mech. Anal. 49, 241–269 (1973).Google Scholar
  8. 8.
    Keller, H. B., & D. S. Cohen, Some positone problems suggested by nonlinear heat generation. J. Math. Mech. 16, 1361–1376 (1967).Google Scholar
  9. 9.
    Krein, M. G., & M. A. Rutman, Linear operators leaving invariant a cone in a Banach space. Amer. Math. Soc. Transl., Ser. 1, 10, 1–128 (1962).Google Scholar
  10. 10.
    Krasnosel'skii, M. A., Positive Solutions of Operator Equations. Groningen: Noordhoff 1964.Google Scholar
  11. 11.
    Laetsch, T., The number of solutions of a nonlinear two point boundary value problem. Indiana Univ. Math. J. 20, 1–13 (1970).Google Scholar
  12. 12.
    Laetsch, T., Uniqueness for sublinear boundary value problems. J. Diff. Equ. 13, 12–23 (1973).Google Scholar
  13. 13.
    Parter, S. V., Solutions of a differential equation arising in chemical reactor processes. The Univ. of Wisconsin Comp. Sci. Dept, Technical Report # 162, 1973.Google Scholar
  14. 14.
    Pimbley, G. H., Jr., A sublinear Sturm-Liouville problem. J. Math. Mech. 11, 121–138 (1962).Google Scholar
  15. 15.
    Protter, M. H., & H. F. Weinberger, Maximum Principles in Differential Equations. Englewood Cliffs, N.J.: Prentice Hall 1967.Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Herbert Amann
    • 1
  1. 1.Mathematisches Institut der Ruhr-UniversitätBochumGermany

Personalised recommendations