TAILIEUCHUNG - Báo cáo hóa học: " A DEGREE THEORY FOR A CLASS OF PERTURBED FREDHOLM MAPS II"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: A DEGREE THEORY FOR A CLASS OF PERTURBED FREDHOLM MAPS II | A DEGREE THEORY FOR A CLASS OF PERTURBED FREDHOLM MAPS II PIERLUIGI BENEVIERI ALESSANDRO CALAMAI AND MASSIMO FURI Received 30 June 2005 Revised 10 October 2005 Accepted 24 October 2005 In a recent paper we gave a notion of degree for a class of perturbations of nonlinear Fredholm maps of index zero between real infinite dimensional Banach spaces. Our purpose here is to extend that notion in order to include the degree introduced by Nussbaum for local a-condensing perturbations of the identity as well as the degree for locally compact perturbations of Fredholm maps of index zero recently defined by the first and third authors. Copyright 2006 Pierluigi Benevieri et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In a recent paper 1 we defined a concept of degree for a special class of noncompact perturbations of nonlinear Fredholm maps of index zero between infinite dimensional real Banach spaces called a-Fredholm maps. The definition of these maps is based on the following two numbers see . 12 associated with a map f o - F from an open subset of a Banach space E to a Banach space F a f sup i f A c o bounded a A 01 a A w f inf i A c o bounded a A o a A where a is the Kuratowski measure of noncompactness in 12 w f is denoted by fi f however we prefer here the more recent notation w f as in 9 . Roughly speaking an a-Fredholm map is of the type f g - k with the inequality a k v g satisfied locally. These maps include locally compact perturbations of Fredholm maps quasi-Fredholm maps for short since when g is Fredholm and k is locally compact Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2006 Article ID 27154 Pages 1-20 DOI FPTA 2006 27154 2 A degree theory for a class of perturbed Fredholm maps II one has a k 0 and w g 0 locally. Moreover they

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