Spectral Theory and Nonlinear Functional Analysis (Chapman & Hall/crc Research Notes in Mathematics Series)

Lopez-Gomez, Julian

CRC Press（2017/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 278 p.
• 言語 ENG
• 商品コード 9781138441972
• DDC分類 515.7

Full Description

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The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers.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.

Contents

Introduction. Bifurcation from Simple Eigenvalues. First General Bifurcation Results. The Algebraic Multiplicity. Fundamental Properties of the Multiplicity. Global Bifurcation Theory. Some Applications. Bibliography.