Annali di Matematica Pura ed Applicata

, Volume 108, Issue 1, pp 329–335 | Cite as

Fredholm mappings and solutions of linear differential equations at singular points

  • Jean Mawhin


Some classical existence theorems for analytic linear differential equations at singular points are shown to be simple consequences of elementary properties of Fredholm mappings.


Differential Equation Singular Point Existence Theorem Simple Consequence Linear Differential Equation 
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  1. [1]
    R. A. Bonic,Linear Functional Analysis, Gordon and Breach, New York (1969).Google Scholar
  2. [2]
    L. Cesari,Functional analysis and Galerkin's method, Michigan Math. J.,14 (1964), pp. 385–414.MathSciNetGoogle Scholar
  3. [3]
    E. A. Coddington -N. Levinson,Theory of Ordinary Differential Equations, Mc Graw-Hill, New York (1955).Google Scholar
  4. [4]
    J. Dieudonné,Foundation of Modern Analysis, Academic Press, New York (1960).Google Scholar
  5. [5]
    J. K. Hale,Applications of Alternative Problems, Brown University Lecture Notes 71-1, Providence (1971).Google Scholar
  6. [6]
    W. A. Harris jr.Y. SibuyaL. Weinberg,Holomorphic solutions of linear differential systems at singular points, Arch. Rat. Mech. Anal.,35 (1969), pp. 245–248.CrossRefMathSciNetGoogle Scholar
  7. [7]
    P. Hartman,Ordinary Differential Equations, Wiley, New York (1964).Google Scholar
  8. [8]
    F. Lettenmeyer,Über die an einer Unbestimmtheitsstelle regulären Lösungen eines Systems homogener linearen Differentialgleichungen, Sitz. Ber. Bayer. Akad. Wiss. Münche, Mat. Nat. Abt. (1926), pp. 287–307.Google Scholar
  9. [9]
    O. Perron,Über diejenigen Integrale linearen Differentialgleichungen, welche sich an einer Unbestimmtheitstelle bestimmt verhalten, Math. Ann.,70 (1911), pp. 1–32.CrossRefzbMATHMathSciNetGoogle Scholar

Supplementary Bibliography

  1. A.
    Yu. F. Korobeinik,Normal solvability of linear differential equations in the complex plane, Math. USSR Izvestija,6 (1972), pp. 445–466. Erratum ibid.,7 (1973), p. 246.CrossRefGoogle Scholar
  2. B.
    B. Malgrange,Sur les points singuliers des équations différentielles, L'Ens. Mathématique,20 (1974), pp. 147–176.zbMATHMathSciNetGoogle Scholar
  3. C.
    L. J. Grimm -L. M. Hall,Holomorphic solutions of functional differential systems near singular points, Proceed. Amer. Math. Soc.,42 (1974), pp. 167–170.CrossRefMathSciNetGoogle Scholar
  4. D.
    L. J. Grimm -L. M. Hall,Holomorphic solutions of singular functional differential equations, J. Math. Anal. Appl.,50 (1975), pp. 627–638.CrossRefMathSciNetGoogle Scholar
  5. E.
    L. J. Grimm -L. M. Hall,An alternative theorem for singular differential systems, J. Differential Equations,18 (1975), pp. 411–422.CrossRefMathSciNetGoogle Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • Jean Mawhin
    • 1
  1. 1.Louvain-La-NeuveBelgium

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