Author : Anonim
Publisher : Unknown
Page : 146 pages
File Size : 44,7 Mb
Release : 1964
Category : Differential equations
ISBN : 0387091149
Lecture Notes in Mathematics
Anonim
Local Theory Of Nonlinear Analytic Ordinary Differential Equations
Local Theory Of Nonlinear Analytic Ordinary Differential Equations Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Local Theory Of Nonlinear Analytic Ordinary Differential Equations book. This book definitely worth reading, it is an incredibly well-written.
Local Theory of Nonlinear Analytic Ordinary Differential Equations
Y. N. Bibikov
Author : Y. N. Bibikov
Publisher : Springer
Page : 155 pages
File Size : 54,8 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540355274
Local Theory of Nonlinear Analytic Ordinary Differential Equations by Y. N. Bibikov Pdf
Local Theory of Nonlinear Analytic Ordinary Differential Equations
Iı̐Uı̐Łrii Nikolaevich Bibikov,Y. N. Bibikov
Author : Iı̐Uı̐Łrii Nikolaevich Bibikov,Y. N. Bibikov
Publisher : Lecture Notes in Mathematics
Page : 166 pages
File Size : 41,5 Mb
Release : 1979-02-05
Category : Mathematics
ISBN : UOM:39015049310371
Local Theory of Nonlinear Analytic Ordinary Differential Equations by Iı̐Uı̐Łrii Nikolaevich Bibikov,Y. N. Bibikov Pdf
Local Methods in Nonlinear Differential Equations
Aleksandr Dmitrievich Bri͡uno
Author : Aleksandr Dmitrievich Bri͡uno
Publisher : Springer
Page : 368 pages
File Size : 41,7 Mb
Release : 1989
Category : Mathematics
ISBN : UOM:39015015724035
Local Methods in Nonlinear Differential Equations by Aleksandr Dmitrievich Bri͡uno Pdf
Local Methods in Nonlinear Differential Equations
Alexander D. Bruno
Author : Alexander D. Bruno
Publisher : Unknown
Page : 348 pages
File Size : 46,7 Mb
Release : 1989-01-01
Category : Differential equations, Nonlinear
ISBN : 3540189262
Local Methods in Nonlinear Differential Equations by Alexander D. Bruno Pdf
The method of normal forms is usually attributed to PoincarA(c) although some of the basic ideas of the method can be found in earlier works of Jacobi, Briot and Bouquet. In this book, A.D.Bruno gives an account of the work of these mathematicians and further developments as well as the results of his own extensive investigations on the subject. The book begins with a thorough presentation of the analytical techniques necessary for the implementation of the theory as well as an extensive description of the geometry of the Newton polygon. It then proceeds to discuss the normal form of systems of ordinary differential equations giving many specific applications of the theory. An underlying theme of the book is the unifying nature of the method of normal forms regarding techniques for the study of the local properties of ordinary differential equations. In the second part of the book it is shown, for a special class of equations, how the method of normal forms yields classical results of Lyapunov concerning families of periodic orbits in the neighborhood of equilibrium points of Hamiltonian systems as well as the more modern results concerning families of quasiperiodic orbits obtained by Kolmogorov, Arnold and Moser. The book is intended for mathematicians, theoretical mechanicians, and physicists. It is suitable for advanced undergraduate and graduate students.
Nonlinear Differential Equations and Dynamical Systems
Feliz Manuel Minhós,João Fialho
Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 48,5 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101
Nonlinear Differential Equations and Dynamical Systems by Feliz Manuel Minhós,João Fialho Pdf
This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
Nonlinear Ordinary Differential Equations
R. Grimshaw
Author : R. Grimshaw
Publisher : CRC Press
Page : 342 pages
File Size : 55,7 Mb
Release : 1991-03-06
Category : Mathematics
ISBN : 0849386071
Nonlinear Ordinary Differential Equations by R. Grimshaw Pdf
Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.
Hamiltonian Systems with Three or More Degrees of Freedom
Carles Simó
Author : Carles Simó
Publisher : Springer Science & Business Media
Page : 681 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401146739
Hamiltonian Systems with Three or More Degrees of Freedom by Carles Simó Pdf
A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.
Local Methods in Nonlinear Differential Equations
Alexander D. Bruno
Author : Alexander D. Bruno
Publisher : Springer
Page : 0 pages
File Size : 48,9 Mb
Release : 1989
Category : Mathematics
ISBN : 3642613144
Local Methods in Nonlinear Differential Equations by Alexander D. Bruno Pdf
The method of normal forms is usually attributed to Poincaré although some of the basic ideas of the method can be found in earlier works of Jacobi, Briot and Bouquet. In this book, A.D.Bruno gives an account of the work of these mathematicians and further developments as well as the results of his own extensive investigations on the subject. The book begins with a thorough presentation of the analytical techniques necessary for the implementation of the theory as well as an extensive description of the geometry of the Newton polygon. It then proceeds to discuss the normal form of systems of ordinary differential equations giving many specific applications of the theory. An underlying theme of the book is the unifying nature of the method of normal forms regarding techniques for the study of the local properties of ordinary differential equations. In the second part of the book it is shown, for a special class of equations, how the method of normal forms yields classical results of Lyapunov concerning families of periodic orbits in the neighborhood of equilibrium points of Hamiltonian systems as well as the more modern results concerning families of quasiperiodic orbits obtained by Kolmogorov, Arnold and Moser. The book is intended for mathematicians, theoretical mechanicians, and physicists. It is suitable for advanced undergraduate and graduate students.
Approaches to the Qualitative Theory of Ordinary Differential Equations
Tong-Ren Ding
Author : Tong-Ren Ding
Publisher : World Scientific
Page : 394 pages
File Size : 50,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812704689
Approaches to the Qualitative Theory of Ordinary Differential Equations by Tong-Ren Ding Pdf
This book is an ideal text for advanced undergraduate students and graduate students with an interest in the qualitative theory of ordinary differential equations and dynamical systems. Elementary knowledge is emphasized by the detailed discussions on the fundamental theorems of the Cauchy problem, fixed-point theorems (especially the twist theorems), the principal idea of dynamical systems, the nonlinear oscillation of Duffing's equation, and some special analyses of particular differential equations. It also contains the latest research by the author as an integral part of the book.
Non Linear Analysis and Boundary Value Problems for Ordinary Differential Equations
F. Zanolin
Author : F. Zanolin
Publisher : Springer
Page : 232 pages
File Size : 53,6 Mb
Release : 1996-12-02
Category : Mathematics
ISBN : UOM:39015049315784
Non Linear Analysis and Boundary Value Problems for Ordinary Differential Equations by F. Zanolin Pdf
The area covered by this volume represents a broad choice of some interesting research topics in the field of dynamical systems and applications of nonlinear analysis to ordinary and partial differential equations. The contributed papers, written by well known specialists, make this volume a useful tool both for the experts (who can find recent and new results) and for those who are interested in starting a research work in one of these topics (who can find some updated and carefully presented papers on the state of the art of the corresponding subject).
Nonlinear Partial Differential Equations
W. F. Ames
Author : W. F. Ames
Publisher : Academic Press
Page : 332 pages
File Size : 53,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483221502
Nonlinear Partial Differential Equations by W. F. Ames Pdf
Nonlinear Partial Differential Equations: A Symposium on Methods of Solution is a collection of papers presented at the seminar on methods of solution for nonlinear partial differential equations, held at the University of Delaware, Newark, Delaware on December 27-29, 1965. The sessions are divided into four Symposia: Analytic Methods, Approximate Methods, Numerical Methods, and Applications. Separating 19 lectures into chapters, this book starts with a presentation of the methods of similarity analysis, particularly considering the merits, advantages and disadvantages of the methods. The subsequent chapters describe the fundamental ideas behind the methods for the solution of partial differential equation derived from the theory of dynamic programming and from finite systems of ordinary differential equations. These topics are followed by reviews of the principles to the lubrication approximation and compressible boundary-layer flow computation. The discussion then shifts to several applications of nonlinear partial differential equations, including in electrical problems, two-phase flow, hydrodynamics, and heat transfer. The remaining chapters cover other solution methods for partial differential equations, such as the synergetic approach. This book will prove useful to applied mathematicians, physicists, and engineers.
Differential Equations with Symbolic Computation
Dongming Wang,Zhiming Zheng
Author : Dongming Wang,Zhiming Zheng
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 48,6 Mb
Release : 2006-03-16
Category : Mathematics
ISBN : 9783764374297
Differential Equations with Symbolic Computation by Dongming Wang,Zhiming Zheng Pdf
This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.
Trends in Theory and Practice of Nonlinear Differential Equations
V. Lakshmikantham
Author : V. Lakshmikantham
Publisher : CRC Press
Page : 589 pages
File Size : 51,7 Mb
Release : 2020-12-17
Category : Mathematics
ISBN : 9781000111095
Trends in Theory and Practice of Nonlinear Differential Equations by V. Lakshmikantham Pdf
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.
The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations
Tran Duc Van,MIko Tsuji,Nguyen Duy Thai Son
Author : Tran Duc Van,MIko Tsuji,Nguyen Duy Thai Son
Publisher : CRC Press
Page : 256 pages
File Size : 46,7 Mb
Release : 1999-06-25
Category : Mathematics
ISBN : 1584880163
The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations by Tran Duc Van,MIko Tsuji,Nguyen Duy Thai Son Pdf
Despite decades of research and progress in the theory of generalized solutions to first-order nonlinear partial differential equations, a gap between the local and the global theories remains: The Cauchy characteristic method yields the local theory of classical solutions. Historically, the global theory has principally depended on the vanishing viscosity method. The authors of this volume help bridge the gap between the local and global theories by using the characteristic method as a basis for setting a theoretical framework for the study of global generalized solutions. That is, they extend the smooth solutions obtained by the characteristic method. The authors offer material previously unpublished in book form, including treatments of the life span of classical solutions, the construction of singularities of generalized solutions, new existence and uniqueness theorems on minimax solutions, differential inequalities of Haar type and their application to the uniqueness of global, semi-classical solutions, and Hopf-type explicit formulas for global solutions. These subjects yield interesting relations between purely mathematical theory and the applications of first-order nonlinear PDEs. The Characteristic Method and Its Generalizations for First-Order Nonlinear Partial Differential Equations represents a comprehensive exposition of the authors' works over the last decade. The book is self-contained and assumes only basic measure theory, topology, and ordinary differential equations as prerequisites. With its innovative approach, new results, and many applications, it will prove valuable to mathematicians, physicists, and engineers and especially interesting to researchers in nonlinear PDEs, differential inequalities, multivalued analysis, differential games, and related topics in applied analysis.