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

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Bibliography

  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. Amann, H., Multiple positive fixed points of asymptotically linear maps. J. Functional Anal., to appear.

  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. 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. 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. Gavalas, G. R., Nonlinear Differential Equations of Chemically Reacting Systems. Berlin-Heidelberg-New York: Springer 1968.

    Google Scholar 

  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. Keller, H. B., & D. S. Cohen, Some positone problems suggested by nonlinear heat generation. J. Math. Mech. 16, 1361–1376 (1967).

    Google Scholar 

  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. Krasnosel'skii, M. A., Positive Solutions of Operator Equations. Groningen: Noordhoff 1964.

    Google Scholar 

  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. Laetsch, T., Uniqueness for sublinear boundary value problems. J. Diff. Equ. 13, 12–23 (1973).

    Google Scholar 

  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.

  14. Pimbley, G. H., Jr., A sublinear Sturm-Liouville problem. J. Math. Mech. 11, 121–138 (1962).

    Google Scholar 

  15. Protter, M. H., & H. F. Weinberger, Maximum Principles in Differential Equations. Englewood Cliffs, N.J.: Prentice Hall 1967.

    Google Scholar 

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  1. Mathematisches Institut der Ruhr-Universität, D-4630, Bochum, Germany

    Herbert Amann

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  1. Herbert Amann
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Communicated by J. Serrin

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Amann, H. On the number of solutions of asymptotically superlinear two point boundary value problems. Arch. Rational Mech. Anal. 55, 207–213 (1974). https://doi.org/10.1007/BF00281748

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  • DOI: https://doi.org/10.1007/BF00281748

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