An introduction to nonlinear functional analysis and elliptic problems / Antonio Ambrosetti, David Arcoya

Auteur: Ambrosetti, Antonio (1944-) - AuteurCo-auteur: Arcoya, David - AuteurType de document: Livre numériqueCollection: Progress in nonlinear differential equations and their applications ; 82Langue: anglaisÉditeur: Boston : Birkhäuser, cop. 2011 ISBN: 9780817681135 Note: This book provides some basic abstract tools used in modern nonlinear analysis in strong relationship with their applications to semilinear elliptic boundary value problems. The content of the book is divided into two parts, which contain 13 chapters. In the first part, key results are discussed 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 of this volume shows how these abstract results apply to Dirichlet elliptic boundary value problems. ... (zbMath) Sujets MSC: 35J60 Partial differential equations -- Elliptic equations and systems -- Nonlinear elliptic equations
46T20 Functional analysis -- Nonlinear functional analysis -- Continuous and differentiable maps
47J30 Operator theory -- Equations and inequalities involving nonlinear operators -- Variational methods
35J20 Partial differential equations -- Elliptic equations and systems -- Variational methods for second-order elliptic equations
35-01 Partial differential equations -- Instructional exposition (textbooks, tutorial papers, etc.)
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This book provides some basic abstract tools used in modern nonlinear analysis in strong relationship with their applications to semilinear elliptic boundary value problems. The content of the book is divided into two parts, which contain 13 chapters. In the first part, key results are discussed 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 of this volume shows how these abstract results apply to Dirichlet elliptic boundary value problems. ... (zbMath)

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