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Approach to a Fifth-Order Boundary Value Problem, via Sperner's Lemma

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DOI: 10.4236/am.2011.28137    3,808 Downloads   7,077 Views  

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

P. Palamides and E. Papageorgiou, "Approach to a Fifth-Order Boundary Value Problem, via Sperner's Lemma," Applied Mathematics, Vol. 2 No. 8, 2011, pp. 993-998. doi: 10.4236/am.2011.28137.

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