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On Bifurcation from Infinity and Multipoint Boundary Value Problems
1African University of Science and Technology (AUST), Abuja, Nigeria 2Institut de Mathematiques et de Sciences Physiques (IMSP), Porto-Novo, Benin
- 1 1African University of Science and Technology (AUST), Abuja, Nigeria 2Institut de Mathematiques et de Sciences Physiques (IMSP), Porto-Novo, Benin
Advances in Pure Mathematics·Volume 04 (2014)·Pages 108–117·Published 9 April 2014·DOI10.4236/apm.2014.44018
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Abstract
We generalize a result on bifurcation from infinity of high order ordinary differential equations with multi-point boundary conditions. Our abstract setting represents a variant of Nonlinear Krein-Ruthman theorems. Furthermore, an analysis of this abstract setting raises an open question motivated by some misunderstanding and inconclusive proofs about the simplicity of principal eigenvalues in some articles in the literature.
KeywordsKrein-RutmanPositivityConeHomogeneityCompactnessEigenvalueSimplicityBifurcation
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