Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 25, pp. 1-14.

Title: Multi point boundary-value problems at resonance for n-order
       differential equations: Positive and monotone solutions
       
Author: Panos K. Palamides (Naval Academy of Greece)

Abstract: 
  In this article, we study a complete $n$-order differential equation
  subject to the $(p,n-p)$ right focal boundary conditions plus an  
  additional nonlocal constrain. We establish sufficient conditions for
  the existence of a family of positive and monotone solutions at resonance.
  The emphasis in this paper is not only that the nonlinearity depends on
  all higher-order derivatives but mainly that the obtaining solution
  satisfies the above extra condition.  Our approach is based on the 
  Sperner's Lemma, proposing in this way  an alternative to the classical 
  methodologies based on fixed point or degree theory and results the 
  introduction of a new set of quite natural hypothesis.

Submitted January 12, 2004. Published February 24, 2004.
Math Subject Classifications: 34B10, 34B18, 34B15, 34G20.
Key Words: Focal boundary value problem; multi-point; resonance; 
    vector field; positive monotone solution; Sperner's lemma;
    Knaster-Kuratowski-Mazurkiewicz's principle.