Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems by Patrick Fitzpatrick 0000-00-00 00:00:00

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by Patrick Fitzpatrick
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Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems by Patrick Fitzpatrick
Author
Patrick Fitzpatrick
Publisher
American Mathematical Society(RI)
Date of release
Pages
131
ISBN
9780821825440
Binding
Hardcover
Illustrations
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PDF, EPUB, MOBI, TXT, DOC
Rating
3
41
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The aim of this work is to develop an additive, integer-valued degree theory for the class of quasilinear Fredholm mappings. This class is sufficiently large that, within its framework, one can study general fully nonlinear elliptic boundary value problems. A degree for the whole class of quasilinear Fredholm mappings must necessarily accomodate sign-switching of the degree along admissible homotopies. The authors introduce "parity", a homotopy invariant of paths of linear Fredholm operators having invertible endpoints. The parity provides a complete description of the possible changes in sign of the degree and thereby permits use of the degree to prove multiplicity and bifurcation theorems for quasilinear Fredholm mappings. Applications are given to the study of fully nonlinear elliptic boundary value problems.

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