Overview

This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems. The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.

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9781138441972

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The book is both an excellent introduction to some novel ideas about nonlinear eigenvalue problems and an exposition of a range of earlier results scattered in different papers and expounded in book form for the first time here. - Mathematical Reviews, Issue 2002 This is a nice introductory text about classical functional analysis... This book will be interesting and useful for many mathematicians, scientists, graduate and undergraduate students. -Mathematical Reviews

Author Information

Julian Lopez-Gomez

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