✦ LIBER ✦
Positive solutions for higher-order Lidstone boundary value problems. A new approach via Sperner's Lemma
✍ Scribed by P.K. Palamides
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 560 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0898-1221
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✦ Synopsis
where f E C ([0, 1] x R~,~+), R+ = [0, ~) associated to the Lidstone boundary conditions
Existence of a solution of boundary value problems (BVP) (1),(2) such that
x(2i)(t)>O, 0 0, 0<t<l, i=0,1 .... ,2n-1.
We further prove analogous results for the case when -f E C([0, 1] x Rn\,R\), 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.