Techniques Of Functional Analysis For Differential And Integral Equations
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Techniques Of Functional Analysis For Differential And Integral Equations
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Author : Paul Sacks
language : en
Publisher: Academic Press
Release Date : 2017-05-16
Techniques Of Functional Analysis For Differential And Integral Equations written by Paul Sacks and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-16 with Mathematics categories.
Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. - Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas - Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations - Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics
Functional Analysis Sobolev Spaces And Partial Differential Equations
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Author : Haim Brezis
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-10
Functional Analysis Sobolev Spaces And Partial Differential Equations written by Haim Brezis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-10 with Mathematics categories.
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.
Applied Functional Analysis And Partial Differential Equations
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Author : Milan Miklavčič
language : en
Publisher: Allied Publishers
Release Date : 1998
Applied Functional Analysis And Partial Differential Equations written by Milan Miklavčič and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Methods In Nonlinear Integral Equations
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Author : R Precup
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Methods In Nonlinear Integral Equations written by R Precup and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.
Integral Equations
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Author : Wolfgang Hackbusch
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Integral Equations written by Wolfgang Hackbusch and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.
Computational Methods For Integral Equations
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Author : L. M. Delves
language : en
Publisher: CUP Archive
Release Date : 1985
Computational Methods For Integral Equations written by L. M. Delves and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
This textbook provides a readable account of techniques for numerical solutions.
Special Functions And Analysis Of Differential Equations
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Author : Praveen Agarwal
language : en
Publisher: CRC Press
Release Date : 2020-09-08
Special Functions And Analysis Of Differential Equations written by Praveen Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-08 with Mathematics categories.
Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.
Nonlinear Functional Analysis And Applications
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Author : Louis B. Rall
language : en
Publisher:
Release Date : 1971
Nonlinear Functional Analysis And Applications written by Louis B. Rall and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
This volume contains the proceedings of an advanced seminar conducted by the Mathematics Research Center at the University of Wisconsin, Madison, held on October 12-14, 1970. This collection of papers is intended to give a reasonably self-contained introduction to the basic concepts and techniques of this field, highlighted by a few significant applications.
Linear And Nonlinear Functional Analysis With Applications
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Author : Philippe G. Ciarlet
language : en
Publisher: SIAM
Release Date : 2013-10-10
Linear And Nonlinear Functional Analysis With Applications written by Philippe G. Ciarlet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-10 with Mathematics categories.
This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.
Implicit Fractional Differential And Integral Equations
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Author : Saïd Abbas
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05
Implicit Fractional Differential And Integral Equations written by Saïd Abbas and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.
This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations