Annali di Matematica Pura ed Applicata

, Volume 103, Issue 1, pp 81–98 | Cite as

Formal aspects of a theory for pairs of linear ordinary differential operators in the regular case

  • Åke Pleijel


The ordinary differential equation Su=λTu containing two operators and a parameter λ is considered on a compact interval. Boundary conditions, homogeneous and non-homogeneous problems, expansions in terms of associated eigenfunctions etc. are parallelled with the classical case when T=1.


Boundary Condition Differential Equation Ordinary Differential Equation Differential Operator Classical Case 
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.


  1. [1]
    G. D. Birkhoff,Boundary value and expansion problems of ordinary differential equations, Transactions of the Amer. Math. Soc.,9 (1908), pp. 373–395.CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    E. L. Ince,Ordinary differential equations, New York, 1926.Google Scholar
  3. [3]
    T. Lalesco,Introduction à la théorie des équations intégrales, Paris, 1912.Google Scholar
  4. [4]
    Å. Pleijel,Quelques problèmes de vibration et les méthodes directes du calcul des variations, Arkiv för Mat., Astr. och Fysik,29 A, No. 23 (1943), pp. 1–17.MathSciNetGoogle Scholar
  5. [5]
    Å. Pleijel,Quelques remarques sur certain problèmes de vibrations dégénérés, Dixième Congrès des Mathématiciens Scandinaves, Copenhague, 1946, pp. 54–58.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1974

Authors and Affiliations

  • Åke Pleijel
    • 1
  1. 1.UppsalaSvezia

Personalised recommendations