ENGLISH

Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems

By Patrick Fitzpatrick , Jacobo Pejsachowicz

Book information

Publisher
Amer Mathematical Society
Year
1993
ISBN
0821825445, 9780821825440
Language
english
Format
PDF
Filesize
8 MB (8771729 bytes)
Series
Memoirs of the American Mathematical Society
Pages
131\145
DPI
600
Orientation
yes
Scanned
yes
Time added
2014-09-08 01:15:22

Description

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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