Memoirs of the American Mathematical Society 1993; 131 pp; softcover Volume: 101 ISBN10: 0821825445 ISBN13: 9780821825440 List Price: US$32 Individual Members: US$19.20 Institutional Members: US$25.60 Order Code: MEMO/101/483
 The aim of this work is to develop an additive, integervalued 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 signswitching 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. Readership Research mathematicians. Table of Contents  Quasilinear Fredholm mappings
 Orientation and the degree
 General properties of the degree
 Mapping theorems
 The parity of a path of linear Fredholm operators
 The regular value formula and homotopy dependence
 Bifurcation and continuation
 Strong orientability
 Fully nonlinear elliptic boundary value problems
