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Showing papers on "Bifurcation diagram published in 1974"




Journal ArticleDOI
TL;DR: In this article, the problem of secondary bifurcation of a branch of eigenfunctions for a nonlinear Hammerstein operator is introduced, and the treatment is restricted to the superlinear and sublinear cases.
Abstract: After some background material, the question of secondary bifurcation of a branch of eigenfunctions for a nonlinear Hammerstein operator is introduced. The treatment is restricted to the superlinear and sublinear cases. The problem of secondary bifurcation arises in the global extension of the solution branches. At our present state of knowledge, we are interested in conditions such that secondary bifurcation does not occur. One of the authors had previously developed a condition against secondary bifurcation. Herein we describe another more straightforward, condition based on well known theorems of perturbation theory. Apres une introduction nous considerons la question des bifurcations secondaires pour une branche de fonctions propres d'un operateur de Hammerstein non-lineaire. La discussion est ici restreinte aux cas superlineaires et sublineaires. Le probleme des bifurcations secondaires se pose dans l'extension globale des solutions. Nous nous interessons actuellement aux conditions qui interdisent les bifurcations secondaires. L'un des auteurs a deja trouve une telle condition. Nous donnons ici une autre condition plus directe, fondee sur des theoremes bien connus de la theorie des perturbations.

4 citations


Book ChapterDOI
01 Jan 1974

1 citations