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Nehari–Calogero–Cohn Inequality

  • Juan Pablo Pinasco
Chapter
  • 947 Downloads
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter, we review the proofs of Nehari, Calogero, and Cohn for Theorem C, together with some generalizations for the p-Laplacian eigenvalues and higher-order problems.

Keywords

Nehari Monotonic Weight Higher Order Linear Differential Equations Lyapunov-type Inequalities Concavity Hypothesis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 17.
    Calogero, F.: Necessary Conditions for the Existence of Bound States. Nuovo Cimento 36, 199–201 (1965)MathSciNetCrossRefGoogle Scholar
  2. 18.
    Calogero, F.: Upper and lower limits for the number of bound states in a given central potential. Communications in Mathematical Physics 1, 80–88 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 28.
    Cohn, J. H. E.: On the Number of Negative Eigen-Values of a Singular Boundary value Problem. J. London Math. Soc. 40, 523–525 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 29.
    Cohn, J. H. E.: On the Number of Negative Eigen-Values of a Singular Boundary Value Problem (II). Journal of the London Mathematical Society, 41, 469–473 (1966)CrossRefzbMATHGoogle Scholar
  5. 81.
    Makai, E.: Über die Nullstellen von Funktionen, die Lösungen Sturm–Liouville’scher Differentialgleichungen sind. Comment. Math. Helv. 16, 153–199 (1944)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 88.
    Nehari, Z.: Some eigenvalue estimates. Journal d’ Analyse Mathematique 7, 79–88 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 89.
    Nehari, Z.: Extremal problems for a class of functionals defined on convex sets. Bull. Amer. Math. Soc. 73, 584–591 (1967)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Juan Pablo Pinasco 2013

Authors and Affiliations

  • Juan Pablo Pinasco
    • 1
  1. 1.Departamento de MatematicaUniversidad de Buenos AiresBuenos AiresArgentina

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