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Annali di Matematica Pura ed Applicata

, Volume 73, Issue 1, pp 195–220 | Cite as

An eigenvalue comparison theorem for second order self-adjoint differential equations

  • John G. Moore
Article
  • 26 Downloads

Summary

This paper is concerned with a comparison of the eigenvalues for pairs of self-adjoint differential systems which arise from a single ordinary second-order differential equation. The sistems differ in the boundary conditions which are imposed, and it is these boundary conditions which will draw most of the attention. The principal results obtained deal with predicting alternation of the eigenvalues for two such systems from the boundary conditions alone, without special consideration of the differential equation.

Keywords

Boundary Condition Differential Equation Special Consideration Differential System Comparison Theorem 
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.

Bibliography

  1. [1]
    G. Birkhoff andS. MacLane,A Survey of Modern Algebra, Revised Edition, The MacMillan Co., New York (1953).Google Scholar
  2. [2]
    O. Bolza,Lectures on the Calculus of Variations, University of Chicago Press, Chicago (1904).Google Scholar
  3. [3]
    M. J. Gottlieb,Oscillation Theorem for Self-Adjoint Boundary Value Problems, Duke Mathematical Journal,15 (1948) 1073–1091.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    M. Morse,The Calculus ot Variations in the Large, American Mathematical Society (1934).Google Scholar

Copyright information

© Nicola Zanichelli Editore 1966

Authors and Affiliations

  • John G. Moore
    • 1
  1. 1.KnoxvilleUSA

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