Orientation and the Leray-Schauder theory for fully nonlinear elliptic boundary value problems
著者
書誌事項
Orientation and the Leray-Schauder theory for fully nonlinear elliptic boundary value problems
（Memoirs of the American Mathematical Society, no. 483）
American Mathematical Society, 1993
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注記
Includes bibliographical references (p. 127-131)
"January 1993, volume 101, number 483 (second of 4 numbers)" -- T.p
内容説明・目次
内容説明
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 accommodate 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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