Nonlinear Functional Analysis and its Applications: II/B: Nonlinear Monotone OperatorsSpringer Science & Business Media, 21 nov 2013 - 741 pagine This is the second of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self -contained and accessible to the nonspecialist. Part II concerns the theory of monotone operators. It is divided into two subvolumes, II/A and II/B, which form a unit. The present Part II/A is devoted to linear monotone operators. It serves as an elementary introduction to the modern functional analytic treatment of variational problems, integral equations, and partial differential equations of elliptic, parabolic and hyperbolic type. This book also represents an introduction to numerical functional analysis with applications to the Ritz method along with the method of finite elements, the Galerkin methods, and the difference method. Many exercises complement the text. The theory of monotone operators is closely related to Hilbert's rigorous justification of the Dirichlet principle, and to the 19th and 20th problems of Hilbert which he formulated in his famous Paris lecture in 1900, and which strongly influenced the development of analysis in the twentieth century. |
Sommario
469 | |
483 | |
484 | |
488 | |
495 | |
Differential Equations | 553 |
CHAPTER 27 | 579 |
CHAPTER 28 | 615 |
CHAPTER 32 | 840 |
CHAPTER 33 | 919 |
GENERAL THEORY OF DISCRETIZATION METHODS | 959 |
CHAPTER 35 | 978 |
CHAPTER 36 | 997 |
Appendix | 1009 |
1119 | |
List of Symbols | 1163 |
Altre edizioni - Visualizza tutto
Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone ... E. Zeidler Anteprima limitata - 2012 |
Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone ... E. Zeidler Anteprima limitata - 1989 |
Nonlinear Functional Analysis and Its Applications: II/ A: Linear Monotone ... E. Zeidler Anteprima non disponibile - 1990 |
Parole e frasi comuni
A-proper A₁ Assume H1 assumptions Banach bifurcation boundary value problem bounded region Browder Chapter classical compact consider const convergence Corollary corresponding definition denotes eigenvalue embedding equivalent Euler equation evolution equations example finite fixed fixed-point Fredholm operator function f Galerkin equation Galerkin method growth condition Hammerstein hemicontinuous Hence Hölder inequality implies index zero integral equations L₂(G Let f Let G Lipschitz continuous lower semicontinuous main theorem Math maximal monotone measure minimal point minimum problem monotone operators Moreover neighborhood nonlinear norm obtain operator equation original problem partial differential equations proof of Theorem real B-space real numbers real reflexive B-space region in RN resp satisfies Section semigroups semilinear sequence Sobolev spaces strictly monotone strongly continuous strongly monotone subset Suppose u₁ unique solution variational inequality variational problem W¹(G yields