TITLE:
Approach to a Fifth-Order Boundary Value Problem, via Sperner's Lemma
AUTHORS:
Panos K. Palamides, Evgenia H. Papageorgiou
KEYWORDS:
Fifth-Order Differential Equation, Vector Field, Kneser’s Theorem, Sperner’s Lemma
JOURNAL NAME:
Applied Mathematics,
Vol.2 No.8,
August
24,
2011
ABSTRACT: We consider the five-point boundary value problem for a fifth-order differential equation, where the nonlinearity is superlinear at both the origin and +infinity. Our method of proof combines the Kneser’s theorem with the well-known from combinatorial topology Sperner’s lemma. We also notice that our geometric approach is strongly based on the associated vector field.