In this paper we consider a certain multipoint-boundary-value-problem and a related eigenvalue-problem the solutions of which are allowed to have spline-character. A representation of the corresponding Green’s function as a spline-interpolation error is derived. If the underlying differential operator is disconjugate this representation leads to the controllability of the sign-structure of the Green’s function. Making use of this result within the theory of partially ordered Banach spaces we get the existence of an eigenvalue of the eigenvalue-problem as well as upper and lower bounds for it.


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Copyright information

© Springer Basel AG 1977

Authors and Affiliations

  • Wolfgang Mackens
    • 1
  1. 1.Institut für MathematikRuhr-Universität BochumBochumDeutschland

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