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Bounds for the lowest critical value of the nonlinear operator-u″+u 3

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Abstract

A method for calculating lower bounds for certain functionals is demonstrated by estimating the first critical value of a special nonlinear operator. The exact solutions of the associated eigenvalue problem are calculated.

Zusammenfassung

Es werden Schranken für den ersten kritischen Wert eines speziellen nichtlinearen Operators berechnet. Dabei wird eine Methode angewendet, mit der sich untere Schranken zu bestimmten Funktionalen berechnen lassen. Zu dem zugehörigen Eigenwertproblem werden die exakten Lösungen bestimmt.

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References

  1. M. Vainberg,Variational Methods for the Study of Nonlinear Operators, Holden Day, San Francisco 1964.

    Google Scholar 

  2. N. Bazley, M. Reeken, andB. Zwahlen,Global Properties of the Minimal Branch of a Class of Nonlinear Variational Problems, Math. Z.123, 301–309 (1971).

    Google Scholar 

  3. N. Bazley andR. Seydel,Existence and Bounds for Critical Energies of the Hartree Operator, Chem. Phys. Lett.24, 128–132 (1974).

    Google Scholar 

  4. A. Weinstein andW. Stenger,Intermediate Problems for Eigenvalues, Academic Press, New York 1972.

    Google Scholar 

  5. N. Bazley Lower Bounds for Eigenvalues, J. Math. Mech.10, 289–307 (1961).

    Google Scholar 

  6. P. Byrd andM. Friedman,Handbook of Elliptic Integrals for Engineers and Physicists, Springer-Verlag, Berlin 1954.

    Google Scholar 

  7. N. Bazley andB. Zwahlen,A Branch of Positive Solutions of Nonlinear Eigenvalue, Problems, Manuscripta Math.2, 365–374 (1970).

    Google Scholar 

  8. D. Sattinger,Topics in Stability and Bifurcation Theory, Lecture Notes 309, Springer-Verlag, Berlin 1973.

    Google Scholar 

  9. R. Bulirsch, J. Stoer, andP. Deuflhard:Numerical Solution of Nonlinear Two-Point Boundary Value Problems I. To appear in Handbook Series Approximation, Num. Math.

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Authors and Affiliations

  1. Mathematisches Institut der Technischen Universität, München, Germany

    Rüdiger Seydel

Authors
  1. Rüdiger Seydel
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Seydel, R. Bounds for the lowest critical value of the nonlinear operator-u″+u 3 . Journal of Applied Mathematics and Physics (ZAMP) 26, 713–720 (1975). https://doi.org/10.1007/BF01596075

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  • DOI: https://doi.org/10.1007/BF01596075

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