Nonlinear Differential Equations In Abstract Spaces

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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

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 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 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.

Nonlinear Differential Equations In Ordered Spaces

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Author : S. Carl
language : en
Publisher: CRC Press
Release Date : 2000-06-14

Nonlinear Differential Equations In Ordered Spaces written by S. Carl and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-06-14 with Mathematics categories.

Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms. By means of these extremality results, the authors prove the existence of extremal solutions between appropriate upper and lower solutions of first and second order discontinuous implicit and explicit ordinary and functional differential equations. They then study the dependence of these extremal solutions on the data. The authors begin by developing an existence theory for an abstract operator equation in ordered spaces and offer new tools for dealing with different kinds of discontinuous implicit and explicit differential equation problems. They present a unified approach to the existence of extremal solutions of quasilinear elliptic and parabolic problems and extend the upper and lower solution method to elliptic and parabolic inclusion of hemivariation type using variational and nonvariational methods. Nonlinear Differential Equations in Ordered Spaces includes research that appears for the first time in book form and is designed as a source book for pure and applied mathematicians. Its self-contained presentation along with numerous worked examples and complete, detailed proofs also make it accessible to researchers in engineering as well as advanced students in these fields.

Nonlinear Operators And Differential Equations In Abstract Spaces

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Author : Yuqing Chen
language : en
Publisher:
Release Date : 2000

Nonlinear Operators And Differential Equations In Abstract Spaces written by Yuqing Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Banach spaces categories.

Stochastic Stability Of Differential Equations In Abstract Spaces

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Author : Kai Liu
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02

Stochastic Stability Of Differential Equations In Abstract Spaces written by Kai Liu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Mathematics categories.

Presents a unified treatment of stochastic differential equations in abstract, mainly Hilbert, spaces.

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.

Monotone Iterative Techniques For Discontinuous Nonlinear Differential Equations

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Author : V. Lakshmikantham
language : en
Publisher: Routledge
Release Date : 2017-09-29

Monotone Iterative Techniques For Discontinuous Nonlinear Differential Equations written by V. Lakshmikantham and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-29 with Mathematics categories.

""Providing the theoretical framework to model phenomena with discontinuous changes, this unique reference presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations and applies this method to derive suitable fixed point theorems in ordered abstract spaces.

Trends In Theory And Practice Of Nonlinear Differential Equations

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Author : V. Lakshmikantham
language : en
Publisher: CRC Press
Release Date : 2020-12-17

Trends In Theory And Practice Of Nonlinear Differential Equations written by V. Lakshmikantham and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.

This book is based on an International Conference on Trends in Theory and Practice of Nonlinear Differential Equations held at The University of Texas at Arlington. It aims to feature recent trends in theory and practice of nonlinear differential equations.