Fredholm Structures, Topological Invariants and Applications
By Messoud Efendiev
The book is a self-contained comprehensive account of the geometrical properties of nonlinear mappings in Banach spaces (and Banach manifolds) associated with Fredholm quasiruled structures. It studies their fundamental properties and related topological invariants, and presents applications to a variety of applied problems. It is to be noted that:
1. The class of mappings, formulated under purely topological hypotheses, is generated by a large class of nonlinear boundary value problems, and
2. The degree theory for such a class of mappings is seen to play a crucial role in detecting multiplicity and bifurcation results for a quite large class of problems arising in mathematical physics.
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Contents Author Bio.
The monograph is mainly addressed to researchers and graduate students interested in the applications of topological methods (new aspects are emphasized) to the global solvability of nonlinear pseudodifferential equations arising in hydrodynamics, continuum mechanics and biology. Even specialists will find something new and interesting, such as the role of the bundle structure of
pseudodifferential operators in the construction of integer-valued degree theory.
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