Abstract
Consider the higher-order nonlinear scalar differential equation ▪ where ▪ associated to the Lidstone boundary conditions ▪ Existence of a solution of boundary value problems (BVP) (1),(2) such that ▪ are given, under superlinear or sublinear growth in f. Similarly, existence for the BVP (1)–(3), under the same assumptions, is proved such that ▪ We further prove analogous results for the case when ▪, i.e., derivatives of the obtaining solution satisfy inverse inequalities. The approach is based on an analysis of the corresponding vector field on the face-plane and the well-known, from combinatorial analysis, Knaster-Kuratowski-Mazurkiewicz's principle or as it is known, Sperner's Lemma.
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