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


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.


Boundary Condition Differential Equation Existence Theorem Differential System Coefficient Function 
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  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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