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Annali di Matematica Pura ed Applicata

, Volume 77, Issue 1, pp 327–335 | Cite as

An existence theorem for non-linear differential systems

  • Sandra Ness Hilt
Article
  • 21 Downloads

Summary

Systems of n non-linear, first-order differential equations, whose coefficient functions satisfy the Carathéodory Conditions, are studied. It is proved that, under certain conditions, the boundedness away from zero of a determinant of a type obtained by R. Conti is sufficient to insure the existence of solutions satisfying n boundary conditions assigned at as many as n points.

Keywords

Boundary Condition Differential Equation Existence Theorem Differential System Coefficient Function 
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.

Literatur

  1. (1).
    I problemi ai limiti lineari generali per i sistemi di equazioni differenziali ordinarie. Un teorema di esistenza, « Boll. U.M.I. », s. III, Vol. VIII, n. 2 (pp. 153–159).Google Scholar
  2. (2).
    C. Carathéodory,Vorlesung über reelle Funktionen (Teubner, 1927). p. 665.Google Scholar
  3. (3).
    See footnote (1).Google Scholar
  4. (4).
    On related difference and differential systems, « Amer. J. Math. », vol. 51 (1929), pp. 265–286.Google Scholar
  5. (5).
    R. Conti,I problemi ai limiti lineari per i sistemi di equazioni differenziali ordinarie: Teoremi di esistenza, « Ann. di Matem. », s. 4, vol. 35 (1953), p. 158.MathSciNetGoogle Scholar
  6. (6).
    E. J. McShane andT. A. Botts,Real Analysis (Princeton, 1959), pp. 92–93.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1967

Authors and Affiliations

  • Sandra Ness Hilt
    • 1
  1. 1.The Colorado CollegeColorado Springs

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