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Z. Hao, L. Liu and L. Debnath, “A Necessary and Sufficiently Condition for the Existence of Positive Solution of Fourth-Order Singular Boundary-Value Problems,” Applied Mathematics Letters, Vol. 16, No. 3, 2003, pp. 279-285. doi:10.1016/S0893-9659(03)80044-7

has been cited by the following article:

• 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.