An introduction to nonlinear analysis and elliptic problem/
Ambrosetti, Antonio.
An introduction to nonlinear analysis and elliptic problem/ Antonio Ambrosetti, David Arcoya - Bostan: Birkhauser, 2011. - xii, 199 p. ; 24 cm. - Progress in nonlinear differential equations and their applications, 82. .
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.
9780817681135
Differential equations, Elliptic
Nonlinear functional analysis
Differentiable dynamical systems
Differential equations, Partial
Functional analysis
Mathematics
515.355 / AMB/I
An introduction to nonlinear analysis and elliptic problem/ Antonio Ambrosetti, David Arcoya - Bostan: Birkhauser, 2011. - xii, 199 p. ; 24 cm. - Progress in nonlinear differential equations and their applications, 82. .
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.
9780817681135
Differential equations, Elliptic
Nonlinear functional analysis
Differentiable dynamical systems
Differential equations, Partial
Functional analysis
Mathematics
515.355 / AMB/I