Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Fitzpatrick, Patrick; Pejsachowicz, Jacobo

Softcover

ISBN 10: 0821825445 ISBN 13: 9780821825440

Publisher: American Mathematical Society, 1993

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1993
• ISBN 10: 0821825445
• ISBN 13: 9780821825440
• Binding: Paperback
• Language: English
• Number of pages: 131