Nonlinear Integral Equations In Abstract Spaces

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Nonlinear Integral Equations In Abstract Spaces

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Author : Dajun Guo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22

Nonlinear Integral Equations In Abstract Spaces written by Dajun Guo 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 2013-11-22 with Mathematics categories.

Many problems arising in the physical sciences, engineering, biology and ap plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces. The theory of nonlinear integral equations in ab stract spaces is a fast growing field with important applications to a number of areas of analysis as well as other branches of science. This book is devoted to a comprehensive treatment of nonlinear integral equations in abstract spaces. It is the first book that is dedicated to a systematic development of this subject, and it includes the developments during recent years. Chapter 1 introduces some basic results in analysis, which will be used in later chapters. Chapter 2, which is a main portion of this book, deals with nonlin ear integral equations in Banach spaces, including equations of Fredholm type, of Volterra type and equations of Hammerstein type. Some applica equations tions to nonlinear differential equations in Banach spaces are given. We also discuss an integral equation modelling infectious disease as a typical applica tion. In Chapter 3, we investigate the first order and second order nonlinear integro-differential equations in Banach spaces including equations of Volterra type and equations of mixed type. Chapter 4 is devoted to nonlinear impulsive integral equations in Banach spaces and their applications to nonlinear impul sive differential equations in Banach spaces.

Differential Equations In Abstract Spaces

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Author : Lakshmikantham
language : en
Publisher: Academic Press
Release Date : 1972-06-16

Differential Equations In Abstract Spaces written by Lakshmikantham and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-06-16 with Computers categories.

Differential Equations in Abstract Spaces

Nonlinear Differential Equations In Abstract Spaces

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Author : V. Lakshmikantham
language : en
Publisher: Pergamon
Release Date : 1981

Nonlinear Differential Equations In Abstract Spaces written by V. Lakshmikantham and has been published by Pergamon this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.

Many problems in partial differential equations which arise from physical models can be considered as ordinary differential equations in appropriate infinite dimensional spaces, for which elegant theories and powerful techniques have recently been developed. This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides. Of special importance is the first systematic presentation of the very important and complex theory of multivalued discontinuous differential equations

Nonlinear Equations In Abstract Spaces

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Author : V. Lakshmikantham
language : en
Publisher: Elsevier
Release Date : 2014-05-27

Nonlinear Equations In Abstract Spaces written by V. Lakshmikantham and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-27 with Mathematics categories.

Many problems in partial differential equations which arise from physical models can be considered as ordinary differential equations in appropriate infinite dimensional spaces, for which elegant theories and powerful techniques have recently been developed. This book gives a detailed account of the current state of the theory of nonlinear differential equations in a Banach space, and discusses existence theory for differential equations with continuous and discontinuous right-hand sides. Of special importance is the first systematic presentation of the very important and complex theory of multivalued discontinuous differential equations.

Nonlinear Integral Equations And Inclusions

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Author : Ravi P. Agarwal
language : en
Publisher: Nova Publishers
Release Date : 2001

Nonlinear Integral Equations And Inclusions written by Ravi P. Agarwal and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

Nonlinear Equations In Abstract Spaces

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Author : Vangipuram Lakshmikantham
language : en
Publisher:
Release Date : 1978

Nonlinear Equations In Abstract Spaces written by Vangipuram Lakshmikantham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Banach spaces categories.

Theory Of Set Differential Equations In Metric Spaces

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Author : V. Lakshmikantham
language : en
Publisher:
Release Date : 2006

Theory Of Set Differential Equations In Metric Spaces written by V. Lakshmikantham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

The aim of this volume is to describe the theory of set differential equations (SDEs) as an independent discipline. It incorporates the recent general theory of set differential equations, discusses the interconnections between set differential equations and fuzzy differential equations and uses both smooth and nonsmooth analysis for investigation. The study of SDEs is a rapidly growing area of mathematics and this volume provides a timely introduction to a subject that follows the present trend of studying analysis and differential equations in metric spaces. It is a useful reference text for postgraduates and researchers/nonlinear analysts, engineering and computational scientists working in fuzzy systems.

Nonlinear Problems In Abstract Cones

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Author : Dajun Guo
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Nonlinear Problems In Abstract Cones written by Dajun Guo and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Notes and Reports in Mathematics in Science and Engineering, Volume 5: Nonlinear Problems in Abstract Cones presents the investigation of nonlinear problems in abstract cones. This book uses the theory of cones coupled with the fixed point index to investigate positive fixed points of various classes of nonlinear operators. Organized into four chapters, this volume begins with an overview of the fundamental properties of cones coupled with the fixed point index. This text then employs the fixed point theory developed to discuss positive solutions of nonlinear integral equations. Other chapters consider several examples from integral and differential equations to illustrate the abstract results. This book discusses as well the fixed points of increasing and decreasing operators. The final chapter deals with the development of the theory of nonlinear differential equations in cones. This book is a valuable resource for graduate students in mathematics. Mathematicians and researchers will also find this book useful.

Nonlinear Functional Evolutions In Banach Spaces

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Author : Ki Sik Ha
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Nonlinear Functional Evolutions In Banach Spaces written by Ki Sik Ha 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 2013-04-17 with Mathematics categories.

There are many problems in nonlinear partial differential equations with delay which arise from, for example, physical models, biochemical models, and social models. Some of them can be formulated as nonlinear functional evolutions in infinite-dimensional abstract spaces. Since Webb (1976) considered autonomous nonlinear functional evo lutions in infinite-dimensional real Hilbert spaces, many nonlinear an alysts have studied for the last nearly three decades autonomous non linear functional evolutions, non-autonomous nonlinear functional evo lutions and quasi-nonlinear functional evolutions in infinite-dimensional real Banach spaces. The techniques developed for nonlinear evolutions in infinite-dimensional real Banach spaces are applied. This book gives a detailed account of the recent state of theory of nonlinear functional evolutions associated with accretive operators in infinite-dimensional real Banach spaces. Existence, uniqueness, and stability for 'solutions' of nonlinear func tional evolutions are considered. Solutions are presented by nonlinear semigroups, or evolution operators, or methods of lines, or inequalities by Benilan. This book is divided into four chapters. Chapter 1 contains some basic concepts and results in the theory of nonlinear operators and nonlinear evolutions in real Banach spaces, that play very important roles in the following three chapters. Chapter 2 deals with autonomous nonlinear functional evolutions in infinite-dimensional real Banach spaces. Chapter 3 is devoted to non-autonomous nonlinear functional evolu tions in infinite-dimensional real Banach spaces. Finally, in Chapter 4 quasi-nonlinear functional evolutions are con sidered in infinite-dimensional real Banach spaces.

Differential Equations In Banach Spaces

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Author : Giovanni Dore
language : en
Publisher: CRC Press
Release Date : 2020-10-07

Differential Equations In Banach Spaces written by Giovanni Dore and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-07 with Mathematics categories.

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.