186,566 research outputs found
Degree theory for C1-Fredholm mappings of index 0
No full textWe develop a degree theory for C 1 Fredholm mappings of index 0 between Banach spaces and Banach manifolds. As in earlier work devoted to the C 2 case, our approach is based upon the concept of parity of a curve of linear Fredholm operators of index 0. This avoids considerations about Fredholm structures involved in other approaches and leads to a theory as complete as that of Leray-Schauder in a much broader setting. In particular, the well-known possible sign change under homotopy is fully elucidated. The technical difficulty arising with C a versus C 2 Fredholm mappings of index 0 is notorious: with only C 1 smoothness, the Sarff-Smale theorem is no longer available to handle crucial issues involving homotopy. In this work, this difficulty is overcome by using a new approximation theorem for C a Fredholm mappings of arbitrary index instead of the Sard-Smale theorem when dealing with homotopie
Orientability of Fredholm families and topological degree
No full textWe construct a degree theory for oriented Fredholm mappings of index zero between open subsets of Banach spaces and between Banach manifolds. Our approach is based on the orientation of Fredholm mappings: it does not use Fredholm structures on the domain and target spaces. We provide a computable formula for the change in degree through an admissible homotopy that is necessary for applications to global bifurcation. The notion of orientation enables us to establish rather precise relationships between our degree and many other degree theories for particular classes of Fredholm maps, including the Elworthy-Tromba degree, which have appeared in the literature in a seemingly unrelated manner
Topological degree for nonlinear Fredholm operators
No full textWe introduce an integer-valued topological degree for proper C2-Fredholm mappings. The changes of the degree under homotopy are described by the parity. We use the degree to prove a global bifurcation theore
Degree theory for proper C^2-Fredholm maps I
No full textWe construct a new integer valued degree theory for proper C2 Fredholm maps of index 0, defined on a simply connected domain. The degree depends on the choice of a point in the domain called "base point". However the change of the base point at most can change the sign of the degree. Also the degree is invariant by homotopy only up to a sig. However the change in degree in both cases is computable using a homotopy invariant of paths of Fredholm operators called parity. We use this in order to extend the Krasnoselskii-Rabinowitz global bifurcation theorem to Fredholm map
RABIER (É.)
No full textDubois Patrick. RABIER (É.). In: Le dictionnaire de pédagogie et d'instruction primaire de Ferdinand Buisson : répertoire biographique des auteurs. Paris : Institut national de recherche pédagogique, 2002. p. 120. (Bibliothèque de l'Histoire de l'Education, 17
A substitute of the Sard-Smale theorem for C^1 -Fredholm mappings.
No full textJOURNAL D'ANALYSE MATHEMATIQU
RABIER (É.)
No full textDubois Patrick. RABIER (É.). In: , . Le dictionnaire de pédagogie et d'instruction primaire de Ferdinand Buisson : répertoire biographique des auteurs. Paris : Institut national de recherche pédagogique, 2002. p. 120. (Bibliothèque de l'Histoire de l'Education, 17
Degree Theory for proper C2-Fredholm maps. Covariant theory.
No full textCongruences for the topological degree of a proper Fredholm map of index 0, covariant under the action of a Lie group are obtained
Elie Rabier. — Leçons de psychologie, 7e édition. — Paris, Hachette
No full textPicavet François. Elie Rabier. — Leçons de psychologie, 7e édition. — Paris, Hachette. In: Revue internationale de l'enseignement, tome 46, Juillet-Décembre 1903. p. 267
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