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

By: Ambrosetti, AntonioContributor(s): Arcoya, DavidMaterial type: Text

TextSeries: Progress in nonlinear differential equations and their applications, 82Publication details: Bostan: Birkhauser, 2011Description: xii, 199 p. ; 24 cmISBN: 9780817681135Subject(s): Differential equations, Elliptic | Nonlinear functional analysis | Differentiable dynamical systems | Differential equations, Partial | Functional analysis | MathematicsDDC classification: 515.355

Contents:

Machine generated contents note: 1.Preliminaries -- 1.1.Sobolev Spaces -- 1.1.1.Embedding Theorems -- 1.2.Linear Elliptic Equations -- 1.2.1.Frechet Differentiability -- 1.2.2.Nemitski Operators -- 1.2.3.Dirichlet Principle -- 1.2.4.Regularity of the Solutions -- 1.2.5.The Inverse of the Laplace Operator -- 1.3.Linear Elliptic Eigenvalue Problems -- 1.3.1.Linear Compact Operators -- 1.3.2.Variational Characterization of The Eigenvalues -- 2.Some Fixed Point Theorems -- 2.1.The Banach Contraction Principle -- 2.2.Increasing Operators -- 3.Local and Global Inversion Theorems -- 3.1.The Local Inversion Theorem -- 3.2.The Implicit Function Theorem -- 3.3.The Lyapunov-Schmidt Reduction -- 3.4.The Global Inversion Theorem -- 3.5.A Global Inversion Theorem with Singularities -- 4.Leray-Schauder Topological Degree -- 4.1.The Brouwer Degree -- 4.2.The Leray-Schauder Topological Degree -- 4.2.1.Index of an Isolated Zero and Computation by Linearization -- 4.3.Continuation Theorem of Leray-Schauder -- 4.3.1.A Topological Lemma -- 4.3.2.A Theorem by Leray and Schauder -- 4.4.Other Continuation Theorems -- 5.An Outline of Critical Points -- 5.1.Definitions -- 5.2.Minima -- 5.3.The Mountain Pass Theorem -- 5.4.The Ekeland Variational Principle -- 5.5.Another Min-Max Theorem -- 5.6.Some Perturbation Results -- 6.Bifurcation Theory -- 6.1.Local Results -- 6.1.1.Bifurcation from a Simple Eigenvalue -- 6.1.2.Bifurcation from an Odd Eigenvalue -- 6.2.Bifurcation for Variational Operators -- 6.2.1.A Krasnoselskii Theorem for Variational Operators -- 6.2.2.Branching Points -- 6.3.Global Bifurcation -- 7.Elliptic Problems and Functional Analysis -- 7.1.Nonlinear Elliptic Problems -- 7.1.1.Classical Formulation -- 7.1.2.Weak Formulation -- 7.2.Sub- and Super-Solutions and Increasing Operators -- 8.Problems with A Priori Bounds -- 8.1.An Elementary Nonexistence Result -- 8.2.Existence of A Priori Bounds -- 8.3.Existence of Solutions -- 8.3.1.Using the Global Inversion Theorem.

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Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
General Books	Central Library, Sikkim University General Book Section	515.355 AMB/I (Browse shelf(Opens below))	Available		P40942

Total holds: 0

Machine generated contents note:
1.Preliminaries --
1.1.Sobolev Spaces --
1.1.1.Embedding Theorems --
1.2.Linear Elliptic Equations --
1.2.1.Frechet Differentiability --
1.2.2.Nemitski Operators --
1.2.3.Dirichlet Principle --
1.2.4.Regularity of the Solutions --
1.2.5.The Inverse of the Laplace Operator --
1.3.Linear Elliptic Eigenvalue Problems --
1.3.1.Linear Compact Operators --
1.3.2.Variational Characterization of The Eigenvalues --
2.Some Fixed Point Theorems --
2.1.The Banach Contraction Principle --
2.2.Increasing Operators --
3.Local and Global Inversion Theorems --
3.1.The Local Inversion Theorem --
3.2.The Implicit Function Theorem --
3.3.The Lyapunov-Schmidt Reduction --
3.4.The Global Inversion Theorem --
3.5.A Global Inversion Theorem with Singularities --
4.Leray-Schauder Topological Degree --
4.1.The Brouwer Degree --
4.2.The Leray-Schauder Topological Degree --
4.2.1.Index of an Isolated Zero and Computation by Linearization --
4.3.Continuation Theorem of Leray-Schauder --
4.3.1.A Topological Lemma --
4.3.2.A Theorem by Leray and Schauder --
4.4.Other Continuation Theorems --
5.An Outline of Critical Points --
5.1.Definitions --
5.2.Minima --
5.3.The Mountain Pass Theorem --
5.4.The Ekeland Variational Principle --
5.5.Another Min-Max Theorem --
5.6.Some Perturbation Results --
6.Bifurcation Theory --
6.1.Local Results --
6.1.1.Bifurcation from a Simple Eigenvalue --
6.1.2.Bifurcation from an Odd Eigenvalue --
6.2.Bifurcation for Variational Operators --
6.2.1.A Krasnoselskii Theorem for Variational Operators --
6.2.2.Branching Points --
6.3.Global Bifurcation --
7.Elliptic Problems and Functional Analysis --
7.1.Nonlinear Elliptic Problems --
7.1.1.Classical Formulation --
7.1.2.Weak Formulation --
7.2.Sub- and Super-Solutions and Increasing Operators --
8.Problems with A Priori Bounds --
8.1.An Elementary Nonexistence Result --
8.2.Existence of A Priori Bounds --
8.3.Existence of Solutions --
8.3.1.Using the Global Inversion Theorem.

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