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Nonlinear Sturm-Liouville problems

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References

  1. Antman, S., General solutions for plane extensible elasticae having nonlinear stress-strain laws. Quart. Appl. Math. 26, 35–47 (1968).

    Google Scholar 

  2. Courant, R., & D. Hilbert, Methods of Mathematical Physics, Vol. I. New York: Interscience 1953.

    Google Scholar 

  3. Friedrichs, K. O., & J. J. Stoker, The nonlinear boundary value problem of the buckled plate. Amer. J. Math. 63, 839–888 (1941).

    Google Scholar 

  4. Ince, E. L., Ordinary Differential Equations. Chap. 10. New York: Dover 1944.

    Google Scholar 

  5. Keller, H. B., J. B. Keller, & E. L. Reiss, Buckled states of circular plates. Quart. App. Math. 20, 55–65 (1962).

    Google Scholar 

  6. Keller, H. B., Buckling of a circular plate under an unusual combined load. S.I.A.M. J. Appl. Math. 14, 1275–1292 (1966).

    Google Scholar 

  7. Keller, J. B., The shape of the strongest column. Arch. Rational Mech. Anal. 5, 275–285 (1960).

    Google Scholar 

  8. Kolodner, I. I., Heavy rotating string — a nonlinear eigenvalue problem. Comm. Pure Appl. Math. 8, 395–408 (1955).

    Google Scholar 

  9. Krasnosel'skii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations. New York: Macmillan 1964.

    Google Scholar 

  10. Ljusternik, L., Sur une classe d'équations différentielles non-linéaires. Mat. Sb. 44, 1143–1168 (1937).

    Google Scholar 

  11. Love, A. E. H., The Mathematical Theory of Elasticity. Chap. 18. New York: Dover 1942.

    Google Scholar 

  12. Nehari, Z., Characteristic values associated with a class of nonlinear second order differential equations. Acta Math. 105, 141–175 (1961).

    Google Scholar 

  13. Odeh, F., & I. Tadjbakhsh, A nonlinear eigenvalue problem for rotating rods. Arch. Rational Mech. Anal. 20, 81–94 (1965).

    Google Scholar 

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

    Google Scholar 

  15. Pimbley, G. H., A super-linear Sturm-Liouville problem. Trans. Amer. Math. Soc. 103, 229–248 (1962).

    Google Scholar 

  16. Reiss, E. L., Bifurcation buckling of spherical caps. Comm. Pure Appl. Math. 18, 65–82 (1965).

    Google Scholar 

  17. Tadjbakhsh, I., & F. Odeh, Equilibrium states of elastic rings. J. Math. Anal. Appl. 18, 59–74 (1967).

    Google Scholar 

  18. Wolkowisky, J. H., Existence of buckled states of circular plates. Comm. Pure Appl. Math. 20, 549–560 (1967).

    Google Scholar 

  19. Wolkowisky, J. H., The Buckling of a Plate on an Elastic Foundation. Thesis, New York University, 1966.

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Authors and Affiliations

  1. Department of Mathematics, University of Colorado, Boulder

    Jay H. Wolkowisky

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  1. Jay H. Wolkowisky
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Communicated by J. Serrin

This paper represents results obtained at the University of Colorado, Boulder, under sponsorship of the Graduate School Computing Center, and at the Courant Institute of Mathematical Sciences, New York University, under the sponsorship of the National Science Foundation, Grant NSF-GP-6724.

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Wolkowisky, J.H. Nonlinear Sturm-Liouville problems. Arch. Rational Mech. Anal. 35, 299–320 (1969). https://doi.org/10.1007/BF00248164

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