Approximation Solvability Of Nonlinear Functional And Differential Equations

Author : Wolodymyr V. Petryshyn
Publisher : Routledge
Page : 227 pages
File Size : 42,6 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351465700

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Approximation-solvability of Nonlinear Functional and Differential Equations by Wolodymyr V. Petryshyn Pdf

This reference/text develops a constructive theory of solvability on linear and nonlinear abstract and differential equations - involving A-proper operator equations in separable Banach spaces, and treats the problem of existence of a solution for equations involving pseudo-A-proper and weakly-A-proper mappings, and illustrates their applications.;Facilitating the understanding of the solvability of equations in infinite dimensional Banach space through finite dimensional appoximations, this book: offers an elementary introductions to the general theory of A-proper and pseudo-A-proper maps; develops the linear theory of A-proper maps; furnishes the best possible results for linear equations; establishes the existence of fixed points and eigenvalues for P-gamma-compact maps, including classical results; provides surjectivity theorems for pseudo-A-proper and weakly-A-proper mappings that unify and extend earlier results on monotone and accretive mappings; shows how Friedrichs' linear extension theory can be generalized to the extensions of densely defined nonlinear operators in a Hilbert space; presents the generalized topological degree theory for A-proper mappings; and applies abstract results to boundary value problems and to bifurcation and asymptotic bifurcation problems.;There are also over 900 display equations, and an appendix that contains basic theorems from real function theory and measure/integration theory.

Author : P. S. Milojevic
Publisher : CRC Press
Page : 288 pages
File Size : 53,7 Mb
Release : 1989-09-28
Category : Mathematics
ISBN : 9781482276916

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Nonlinear Functional Analysis by P. S. Milojevic Pdf

This book is based on the lectures presented at the Special Session on Nonlinear Functional Analysis of the American Mathematical Society Regional Meeting, held at New Jersey Institute of Technology. It explores global invertibility and finite solvability of nonlinear differential equations.

Author : Irena Rachunkova,Svatoslav Stanek,Milan Tvrdy
Publisher : Hindawi Publishing Corporation
Page : 279 pages
File Size : 45,6 Mb
Release : 2009
Category : Boundary value problems
ISBN : 9789774540400

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Solvability of Nonlinear Singular Problems for Ordinary Differential Equations by Irena Rachunkova,Svatoslav Stanek,Milan Tvrdy Pdf

Author : Jacques Louis Lions
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 47,8 Mb
Release : 2011-06-07
Category : Mathematics
ISBN : 9783642110573

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Numerical Analysis of Partial Differential Equations by Jacques Louis Lions Pdf

S. Albertoni: Alcuni metodi di calcolo nella teoria della diffusione dei neutroni.- I. Babuska: Optimization and numerical stability in computations.- J.H. Bramble: Error estimates in elliptic boundary value problems.- G. Capriz: The numerical approach to hydrodynamic problems.- A. Dou: Energy inequalities in an elastic cylinder.- T. Doupont: On the existence of an iterative method for the solution of elliptic difference equation with an improved work estimate.- J. Douglas, J.R. Cannon: The approximation of harmonic and parabolic functions of half-spaces from interior data.- B.E. Hubbard: Error estimates in the fixed Membrane problem.- K. Jorgens: Calculation of the spectrum of a Schrödinger operator.- A. Lasota: Contingent equations and boundary value problems.- J.L. Lions: Réduction à des problèmes du type Cauchy-Kowalewska.- J.L. Lions: Problèmes aux limites non homogènes à données irrégulières; une méthode d’approximation.- J.L. Lions: Remarques sur l’approximation régularisée de problèmes aux limites.- W.V. Petryshyn: On the approximation-solvability of nonlinear functional equations in normed linear spaces.- P.A. Raviart: Approximation des équations d’évolution par des méthodes variationnelles.- M. Sibony, H. Brezis: Méthodes d’approximation et d’itération pour les operateurs monotones.- V. Thomee: Some topics in stability theory for partial difference operators.

Author : Antonio Ambrosetti,Kung-ching Chang,Ivar Ekeland
Publisher : World Scientific
Page : 298 pages
File Size : 42,8 Mb
Release : 1998-09-02
Category : Electronic
ISBN : 9789814544856

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Nonlinear Functional Analysis And Applications To Differential Equations: Proceedings Of The Second School by Antonio Ambrosetti,Kung-ching Chang,Ivar Ekeland Pdf

This advanced level textbook is devoted to the description of systems which show ordered magnetic phases. A wide selection of topics is covered, including a detailed treatment of the mean-field approximation as the main paradigm for the phenomenological description of phase transitions. The book discusses the properties of low-dimensional systems and uses Green's functions extensively after a useful mathematical introduction. A thorough presentation of the RKKY and related models of indirect exchange is also featured, and a chapter on surface magnetism, rarely found in other textbooks, adds to the uniqueness of this book.For the second edition, three new chapters have been added, namely on magnetic anisotropy, on coherent magnon states and on local moments. Additionally, the chapter on itinerant magnetism has been enlarged by including a section on paramagnons.

Author : Louis B. Rall
Publisher : Elsevier
Page : 595 pages
File Size : 50,7 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483272443

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Nonlinear Functional Analysis and Applications by Louis B. Rall Pdf

Nonlinear Functional Analysis and Applications provides information pertinent to the fundamental aspects of nonlinear functional analysis and its application. This book provides an introduction to the basic concepts and techniques of this field. Organized into nine chapters, this book begins with an overview of the possibilities for applying ideas from functional analysis to problems in analysis. This text then provides a systematic exposition of several aspects of differential calculus in norms and topological linear spaces. Other chapters consider the various settings in nonlinear functional analysis in which differentials play a significant role. This book discusses as well the generalized inverse for a bounded linear operator, whose range is not necessarily closed. The final chapter deals with the equations of hydrodynamics, which are usually highly nonlinear and difficult to solve. This book is a valuable resource for mathematicians. Readers who are interested in nonlinear functional analysis will also find this book useful.

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 52,6 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

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Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Author : Gennadii V. Demidenko,Stanislav V. Upsenskii
Publisher : CRC Press
Page : 506 pages
File Size : 43,8 Mb
Release : 2003-04-25
Category : Mathematics
ISBN : 9780824748517

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Partial Differential Equations And Systems Not Solvable With Respect To The Highest-Order Derivative by Gennadii V. Demidenko,Stanislav V. Upsenskii Pdf

This text introduces a classification of equations and systems not solved with respect to the higher-order derivative, and studies boundary-value problems for these classes of equations. It includes mathematical results from S.L. Sobolev's study on the small oscillations of a rotating fluid.

Author : Mingjun Chen,Zhongying Chen,Guanrong Chen
Publisher : World Scientific
Page : 360 pages
File Size : 52,7 Mb
Release : 1997-07-01
Category : Mathematics
ISBN : 9789814497695

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Approximate Solutions of Operator Equations by Mingjun Chen,Zhongying Chen,Guanrong Chen Pdf

This book offers an elementary and self-contained introduction to many fundamental issues concerning approximate solutions of operator equations formulated in an abstract Banach space setting, including important topics such as solvability, computational schemes, convergence, stability and error estimates. The operator equations under investigation include various linear and nonlinear types of ordinary and partial differential equations, integral equations, and abstract evolution equations, which are frequently involved in applied mathematics and engineering applications. Each chapter contains well-selected examples and exercises, for the purposes of demonstrating the fundamental theories and methods developed in the text and familiarizing the reader with functional analysis techniques useful for numerical solutions of various operator equations. Contents:IntroductionOperator Equations and Their Approximate Solutions (I): Compact Linear OperatorsOperator Equations and Their Approximate solutions (II): Other Linear OperatorsTopological Degrees and Fixed Point EquationsNonlinear Monotone Operator Equations and Their Approximate SolutionsOperator Evolution Equations and Their Projective Approximate Solutions Readership: Applied mathematicians, mathematical physicists, numerical analysts and electrical & mechanical engineers. keywords:Operator Evolution Equation;Nonlinear Operator Equation;Monotone Operator;Projective Approximation;Least-Squares Algorithm;Topological Degree;Fixed Point Theorem

Author : Jacques Louis Lions
Publisher : Springer
Page : 478 pages
File Size : 43,9 Mb
Release : 2011-03-30
Category : Electronic
ISBN : 3642110584

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Numerical Analysis of Partial Differential Equations by Jacques Louis Lions Pdf

S. Albertoni: Alcuni metodi di calcolo nella teoria della diffusione dei neutroni.- I. Babuska: Optimization and numerical stability in computations.- J.H. Bramble: Error estimates in elliptic boundary value problems.- G. Capriz: The numerical approach to hydrodynamic problems.- A. Dou: Energy inequalities in an elastic cylinder.- T. Doupont: On the existence of an iterative method for the solution of elliptic difference equation with an improved work estimate.- J. Douglas, J.R. Cannon: The approximation of harmonic and parabolic functions of half-spaces from interior data.- B.E. Hubbard: Error estimates in the fixed Membrane problem.- K. Jorgens: Calculation of the spectrum of a Schr dinger operator.- A. Lasota: Contingent equations and boundary value problems.- J.L. Lions: R duction des probl mes du type Cauchy-Kowalewska.- J.L. Lions: Probl mes aux limites non homog nes donn es irr guli res; une m thode d approximation.- J.L. Lions: Remarques sur l approximation r gularis e de probl mes aux limites.- W.V. Petryshyn: On the approximation-solvability of nonlinear functional equations in normed linear spaces.- P.A. Raviart: Approximation des quations d volution par des m thodes variationnelles.- M. Sibony, H. Brezis: M thodes d approximation et d it ration pour les operateurs monotones.- V. Thomee: Some topics in stability theory for partial difference operators.

Author : T. A. Burton
Publisher : Courier Corporation
Page : 370 pages
File Size : 41,5 Mb
Release : 2014-06-24
Category : Mathematics
ISBN : 9780486150451

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Stability & Periodic Solutions of Ordinary & Functional Differential Equations by T. A. Burton Pdf

This book's discussion of a broad class of differential equations includes linear differential and integrodifferential equations, fixed-point theory, and the basic stability and periodicity theory for nonlinear ordinary and functional differential equations.

Author : Roger Temam
Publisher : SIAM
Page : 147 pages
File Size : 55,5 Mb
Release : 1995-01-01
Category : Technology & Engineering
ISBN : 9780898713404

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Navier-Stokes Equations and Nonlinear Functional Analysis by Roger Temam Pdf

This second edition attempts to arrive as simply as possible at some central problems in the Navier-Stokes equations.

Author : Martin Hermann,Masoud Saravi
Publisher : Springer
Page : 310 pages
File Size : 42,8 Mb
Release : 2016-05-09
Category : Mathematics
ISBN : 9788132228127

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Nonlinear Ordinary Differential Equations by Martin Hermann,Masoud Saravi Pdf

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march method. This book comprehensively investigates various new analytical and numerical approximation techniques that are used in solving nonlinear-oscillator and structural-system problems. Students often rely on the finite element method to such an extent that on graduation they have little or no knowledge of alternative methods of solving problems. To rectify this, the book introduces several new approximation techniques.

Author : Pierluigi Colli,Angelo Favini,Elisabetta Rocca,Giulio Schimperna,Jürgen Sprekels
Publisher : Springer
Page : 571 pages
File Size : 47,6 Mb
Release : 2017-11-03
Category : Mathematics
ISBN : 9783319644899

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Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs by Pierluigi Colli,Angelo Favini,Elisabetta Rocca,Giulio Schimperna,Jürgen Sprekels Pdf

This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.

Author : Hiroki Tanabe
Publisher : CRC Press
Page : 431 pages
File Size : 47,7 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351446877

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Functional Analytic Methods for Partial Differential Equations by Hiroki Tanabe Pdf

Combining both classical and current methods of analysis, this text present discussions on the application of functional analytic methods in partial differential equations. It furnishes a simplified, self-contained proof of Agmon-Douglis-Niremberg's Lp-estimates for boundary value problems, using the theory of singular integrals and the Hilbert transform.