Linear Equations in Banach Spaces
Linear Equations in Banach Spaces

Author: KREIN

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 112

ISBN-13: 1468480685

DOWNLOAD EBOOK

INTRODUCTION . . . . . . xiii § 1. LINEAR EQUATIONS. BASIC NOTIONS . 3 § 2. EQUATIONS WITH A CLOSED OPERATOR 6 § 3. THE ADJOINT EQUATION . . . . . . 10 § 4. THE EQUATION ADJOINT TO THE FACTORED EQUATION. 17 § 5. AN EQUATION WITH A CLOSED OPERATOR WHICH HAS A DENSE DOMAIN 18 NORMALLY SOLVABLE EQUATIONS WITH FINITE DIMENSIONAL KERNEL. 22 § 6. A PRIORI ESTIMATES .. . . . . . 24 § 7. EQUATIONS WITH FINITE DEFECT . . . 27 § 8. § 9. SOME DIFFERENT ADJOINT EQUATIONS . 30 § 10. LINEAR TRANSFORMATIONS OF EQUATIONS 33 TRANSFORMATIONS OF d-NORMAL EQUATIONS . 38 § 11. § 12. NOETHERIAN EQUATIONS. INDEX. . . . . . 42 § 13. EQUATIONS WITH OPERATORS WHICH ACT IN A SINGLE SPACE 44 § 14. FREDHOLM EQUATIONS. REGULARIZATION OF EQUATIONS 46 § 15. LINEAR CHANGES OF VARIABLE . . . . . . . . 50 § 16. STABILITY OF THE PROPERTIES OF AN EQUATION 53 OVERDETERMINED EQUATIONS 59 § 17. § 18. UNDETERMINED EQUATIONS 62 § 19. INTEGRAL EQUATIONS . . . 65 DIFFERENTIAL EQUATIONS . 80 § 20. APPENDIX. BASIC RESULTS FROM FUNCTIONAL ANALYSIS USED IN THE TEXT 95 LITERATURE CITED . . . . . . . . . . . . . . . . . . .. . . . 99 . . PRE F ACE The basic material appearing in this book represents the substance v of a special series of lectures given by the author at Voronez University in 1968/69, and, in part, at Dagestan University in 1970.

Nonlinear Differential Equations of Monotone Types in Banach Spaces
Nonlinear Differential Equations of Monotone Types in Banach Spaces

Author: Viorel Barbu

Publisher: Springer Science & Business Media

Published: 2010-01-01

Total Pages: 283

ISBN-13: 1441955429

DOWNLOAD EBOOK

This monograph is concerned with the basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. It focuses on major results in recent decades.

Evolution Equations
Evolution Equations

Author: Gisele Ruiz Goldstein

Publisher: CRC Press

Published: 2003-06-24

Total Pages: 442

ISBN-13: 9780824709754

DOWNLOAD EBOOK

Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.

Functional Analysis, Sobolev Spaces and Partial Differential Equations
Functional Analysis, Sobolev Spaces and Partial Differential Equations

Author: Haim Brezis

Publisher: Springer Science & Business Media

Published: 2010-11-02

Total Pages: 600

ISBN-13: 0387709142

DOWNLOAD EBOOK

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.

Second Order Linear Differential Equations in Banach Spaces
Second Order Linear Differential Equations in Banach Spaces

Author: H.O. Fattorini

Publisher: Elsevier

Published: 2011-08-18

Total Pages: 329

ISBN-13: 0080872190

DOWNLOAD EBOOK

Second order linear differential equations in Banach spaces can be used for modelling such second order equations of mathematical physics as the wave equation, the Klein-Gordon equation, et al. In this way, a unified treatment can be given to subjects such as growth of solutions, singular perturbation of parabolic, hyperbolic and Schrödinger type initial value problems, and the like. The book covers in detail these subjects as well as the applications to each specific problem.

Monotone Operators in Banach Space and Nonlinear Partial Differential Equations
Monotone Operators in Banach Space and Nonlinear Partial Differential Equations

Author: R. E. Showalter

Publisher: American Mathematical Soc.

Published: 2013-02-22

Total Pages: 296

ISBN-13: 0821893971

DOWNLOAD EBOOK

The objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces. A highlight of this presentation is the large number and variety of examples introduced to illustrate the connection between the theory of nonlinear operators and partial differential equations. These include primarily semilinear or quasilinear equations of elliptic or of parabolic type, degenerate cases with change of type, related systems and variational inequalities, and spatial boundary conditions of the usual Dirichlet, Neumann, Robin or dynamic type. The discussions of evolution equations include the usual initial-value problems as well as periodic or more general nonlocal constraints, history-value problems, those which may change type due to a possibly vanishing coefficient of the time derivative, and other implicit evolution equations or systems including hysteresis models. The scalar conservation law and semilinear wave equations are briefly mentioned, and hyperbolic systems arising from vibrations of elastic-plastic rods are developed. The origins of a representative sample of such problems are given in the appendix.

Differential Equations in Banach Spaces
Differential Equations in Banach Spaces

Author: Giovanni Dore

Publisher: CRC Press

Published: 2020-10-08

Total Pages: 290

ISBN-13: 1000153657

DOWNLOAD EBOOK

This reference - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations.;With contributions from international experts, Differential Equations in Banach Spaces is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.