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An Introduction to Nonlinear Functional Analysis and Elliptic Problems : Introduction to Nonlinear Functional Analysis and Elliptic Problems - Antonio Ambrosetti

An Introduction to Nonlinear Functional Analysis and Elliptic Problems

Introduction to Nonlinear Functional Analysis and Elliptic Problems

By: Antonio Ambrosetti, David Arcoya Álvarez

eText | 19 July 2011

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This self-contained textbook provides the basic, abstract??tools??used in??nonlinear analysis??and their applications to semilinear elliptic boundary value problems.??By first??outlining the advantages and disadvantages of each method, this comprehensive text??displays how various??approaches??can easily be??applied??to a range of model cases.An Introduction to Nonlinear Functional Analysis and Elliptic Problems??is divided into two parts: the first discusses key??results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, Leray Schauder degree, critical point theory, and bifurcation theory; the second part shows how these abstract results apply to Dirichlet elliptic boundary value problems. The exposition is driven by numerous prototype problems and exposes a variety of approaches to??solving them.Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a??practical text for an introductory course or seminar on nonlinear functional analysis.
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Non-FictionMathematicsCalculus & Mathematical AnalysisDifferential Calculus & EquationsFunctional Analysis & TransformsReference, Information & Interdisciplinary SubjectsResearch & InformationInformation theoryCybernetics & Systems Theory

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