Series: Progress in Nonlinear Differential Equations and Their Applications, Vol. 82
2011, XII, 199 p. 12 illus.
ISBN 978-0-8176-8113-5
Provides the basic, abstract tools used in nonlinear analysis
Presents 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
Outlines a variety of approaches and displays how they can easily be applied to a range of model cases
Clear exposition driven by numerous prototype problems
An extensive appendix that includes further results on weak derivatives
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.
Series: Frontiers in Mathematics
2011, 210 p.Softcover,
ISBN 978-3-0348-0193-5
Due: September 30, 2011
This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.
Content Level ≫ Research
Related subjects ≫ Analysis
Preface.- Some notes on trigonometric approximation.- The end points effect.- Looking for new moduli.- Exact estimates and asymptotic.- Construction of special operators.- Bibliography.
Series: Springer Monographs in Mathematics
2011, XVIII, 397 p. 10 illus., 4 in color.
Hardcover, ISBN 978-3-642-22663-2
Due: October 31, 2011
The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields who are interested in phenomena modeled by nonlinear partial differential equations.?
Content Level ≫ Research
Keywords ≫ 35-02, 49-02, 92-02, 58-02, 37-02, 35Qxx - degenerate and singular phenomena - mathematical biology - partial differential equations - population genetics
Related subjects ≫ Analysis - Dynamical Systems & Differential Equations - Mathematics
Viorel Barbu: Foreword.- 1.Overview of merhods in PDEs.- 2.Liouville Type Theorems for Elliptic Operators in Divergence Form.- 3.Blow-up Boundary Solutions.- 4.Singular Lane-Emden-Fowler Equations and Systems.- 5.Singular Elliptic Inequalities in Exterior Domains.- 6.Two Quasilinear Elliptic Problems.- 7.Some Classes of Polyharmonic Problems.- 8.Large Time Behavior of Solutions for Degenerate Parabolic Equations.- 9.Rection-Diffusion Systems in Chemistry.- 10.Pattern Formation and Gierer-Meinhardt Model.- Appendices.- References.- Index.
Series: Graduate Texts in Mathematics, Vol. 262
2011, XII, 244 p.
Hardcover, ISBN 978-1-4614-1134-5
Due: September 28, 2011
Essentials of Integration Theory for Analysis is a substantial revision of the best-selling Birkhauser title by the same author, A Concise Introduction to the Theory of Integration. Highlights of this new textbook for the GTM series include revisions to Chapter 1 which add a section about the rate of convergence of Riemann sums and introduces a discussion of the Euler?MacLauren formula. In Chapter 2, where Lebesque’s theory is introduced, a construction of the countably additive measure is done with sufficient generality to cover both Lebesque and Bernoulli measures. Chapter 3 includes a proof of Lebesque’s differential theorem for all monotone functions and the concluding chapter has been expanded to include a proof of Caratheory’s method for constructing measures and his result is applied to the construction of the Hausdorff measures.
This new gem is appropriate as a text for a one-semester graduate course in integration theory and is complimented by the addition of several problems related to the new material. The text is also highly useful for self-study. A complete solutions manual is available for instructors who adopt the text for their courses.
-Preface.-1. The Classical Theory.-2. Measures. -3. Lebesgue Integration.-4. Products of Measures.-5. Changes of Variable.-6. Basic Inequalities and Lebesgue Spaces.-7. Hilbert Space and Elements of Fourier Analysis.-8. The Radon-Nikodym Theorem, Daniell Integration, and Caratheodory's Extension Theorem.-Index.
Series: Lecture Notes in Mathematics, Vol. 2030
2011, XVI, 238 p. 56 illus.
Softcover, ISBN 978-3-642-22533-8
Due: August 31, 2011
The first part of the book studies pseudo-periodic maps of a closed surface of genus greater than or equal to two. This class of homeomorphisms was originally introduced by J. Nielsen in 1944 as an extension of periodic maps. In this book, the conjugacy classes of the (chiral) pseudo-periodic mapping classes are completely classified, and Nielsen’s incomplete classification is corrected. The second part applies the results of the first part to the topology of degeneration of Riemann surfaces. It is shown that the set of topological types of all the singular fibers appearing in one-parameter holomorphic families of Riemann surfaces is in a bijective correspondence with the set of conjugacy classes of the pseudo-periodic maps of negative twists. The correspondence is given by the topological monodromy.
Part I: Conjugacy Classification of Pseudo-periodic Mapping Classes.- 1 Pseudo-periodic Maps.- 2 Standard Form.- 3 Generalized Quotient.- 4 Uniqueness of Minimal Quotient.- 5 A Theorem in Elementary Number Theory.- 6 Conjugacy Invariants.- Part II: The Topology of Degeneration of Riemann Surfaces.- 7 Topological Monodromy.- 8 Blowing Down Is a Topological Operation.- 9 Singular Open-Book.
Series: Springer Monographs in Mathematics
3rd rev. and enlarged ed., 2012, X, 353 p.
Hardcover, ISBN 978-94-007-2246-0
Due: October 11, 2011
An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application.
This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems.
Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.
Fundamentals of Functional Analysis.- Convex Functions.- Convex Programming.- Convex Control Problems in Banach Spaces