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Qualitative Study Of Nonlinear Difference Equations
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Book Synopsis A First Course in the Qualitative Theory of Differential Equations by : James Hetao Liu
Download or read book A First Course in the Qualitative Theory of Differential Equations written by James Hetao Liu and published by . This book was released on 2003 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete analysis of those subjects that are of fundamental importance to the qualitative theory of differential equations and related to current research-including details that other books in the field tend to overlook. Chapters 1-7 cover the basic qualitative properties concerning existence and uniqueness, structures of solutions, phase portraits, stability, bifurcation and chaos. Chapters 8-12 cover stability, dynamical systems, and bounded and periodic solutions. A good reference book for teachers, researchers, and other professionals.
Book Synopsis Qualitative Analysis of Delay Partial Difference Equations by : B. G. Zhang
Download or read book Qualitative Analysis of Delay Partial Difference Equations written by B. G. Zhang and published by Hindawi Publishing Corporation. This book was released on 2007 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Difference Equations and Their Applications by : A.N. Sharkovsky
Download or read book Difference Equations and Their Applications written by A.N. Sharkovsky and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of difference equations is now enjoying a period of Renaissance. Witness the large number of papers in which problems, having at first sight no common features, are reduced to the investigation of subsequent iterations of the maps f· IR. m ~ IR. m, m > 0, or (which is, in fact, the same) to difference equations The world of difference equations, which has been almost hidden up to now, begins to open in all its richness. Those experts, who usually use differential equations and, in fact, believe in their universality, are now discovering a completely new approach which re sembles the theory of ordinary differential equations only slightly. Difference equations, which reflect one of the essential properties of the real world-its discreteness-rightful ly occupy a worthy place in mathematics and its applications. The aim of the present book is to acquaint the reader with some recently discovered and (at first sight) unusual properties of solutions for nonlinear difference equations. These properties enable us to use difference equations in order to model complicated os cillating processes (this can often be done in those cases when it is difficult to apply ordinary differential equations). Difference equations are also a useful tool of syn ergetics- an emerging science concerned with the study of ordered structures. The application of these equations opens up new approaches in solving one of the central problems of modern science-the problem of turbulence.
Book Synopsis Nonlinear Difference Equations by : H. Sedaghat
Download or read book Nonlinear Difference Equations written by H. Sedaghat and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is generally acknowledged that deterministic formulations of dy namical phenomena in the social sciences need to be treated differently from similar formulations in the natural sciences. Social science phe nomena typically defy precise measurements or data collection that are comparable in accuracy and detail to those in the natural sciences. Con sequently, a deterministic model is rarely expected to yield a precise description of the actual phenomenon being modelled. Nevertheless, as may be inferred from a study of the models discussed in this book, the qualitative analysis of deterministic models has an important role to play in understanding the fundamental mechanisms behind social sci ence phenomena. The reach of such analysis extends far beyond tech nical clarifications of classical theories that were generally expressed in imprecise literary prose. The inherent lack of precise knowledge in the social sciences is a fun damental trait that must be distinguished from "uncertainty. " For in stance, in mathematically modelling the stock market, uncertainty is a prime and indispensable component of a model. Indeed, in the stock market, the rules are specifically designed to make prediction impossible or at least very difficult. On the other hand, understanding concepts such as the "business cycle" involves economic and social mechanisms that are very different from the rules of the stock market. Here, far from seeking unpredictability, the intention of the modeller is a scientific one, i. e.
Book Synopsis Applications of Nonlinear Analysis by : Themistocles M. Rassias
Download or read book Applications of Nonlinear Analysis written by Themistocles M. Rassias and published by Springer. This book was released on 2018-06-29 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt: New applications, research, and fundamental theories in nonlinear analysis are presented in this book. Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory. Topics include: Fixed point theory Fixed-circle theory Coupled fixed points Nonlinear duality in Banach spaces Jensen's integral inequality and applications Nonlinear differential equations Nonlinear integro-differential equations Quasiconvexity, Stability of a Cauchy-Jensen additive mapping Generalizations of metric spaces Hilbert-type integral inequality, Solitons Quadratic functional equations in fuzzy Banach spaces Asymptotic orbits in Hill’sproblem Time-domain electromagnetics Inertial Mann algorithms Mathematical modelling Robotics Graduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. Research scientists and engineers studying essential modern methods and techniques to solve a variety of problems will find this book a valuable source filled with examples that illustrate concepts.
Book Synopsis Dynamics of Second Order Rational Difference Equations by : Mustafa R.S. Kulenovic
Download or read book Dynamics of Second Order Rational Difference Equations written by Mustafa R.S. Kulenovic and published by CRC Press. This book was released on 2001-07-30 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph provides systematic, instructive analysis of second-order rational difference equations. After classifying the various types of these equations and introducing some preliminary results, the authors systematically investigate each equation for semicycles, invariant intervals, boundedness, periodicity, and global stabili
Book Synopsis Global Behavior of Nonlinear Difference Equations of Higher Order with Applications by : V.L. Kocic
Download or read book Global Behavior of Nonlinear Difference Equations of Higher Order with Applications written by V.L. Kocic and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear difference equations of order greater than one are of paramount impor tance in applications where the (n + 1)st generation (or state) of the system depends on the previous k generations (or states). Such equations also appear naturally as discrete analogues and as numerical solutions of differential and delay differential equations which model various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our aim in this monograph is to initiate a systematic study of the global behavior of solutions of nonlinear scalar difference equations of order greater than one. Our primary concern is to study the global asymptotic stability of the equilibrium solution. We are also interested in whether the solutions are bounded away from zero and infinity, in the description of the semi cycles of the solutions, and in the existence of periodic solutions. This monograph contains some recent important developments in this area together with some applications to mathematical biology. Our intention is to expose the reader to the frontiers of the subject and to formulate some important open problems that require our immediate attention.
Book Synopsis Difference Equations and Inequalities by : Ravi P. Agarwal
Download or read book Difference Equations and Inequalities written by Ravi P. Agarwal and published by CRC Press. This book was released on 2000-01-27 with total page 1010 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of difference equations and inequalities. This second edition offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, sociology, and
Book Synopsis Dynamic Equations on Time Scales by : Martin Bohner
Download or read book Dynamic Equations on Time Scales written by Martin Bohner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: On becoming familiar with difference equations and their close re lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Lecture Notes 312 (page 10), 1973] A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both. [E. T. BELL, Men of Mathematics, Simon and Schuster, New York (page 13/14), 1937] The theory of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in his PhD thesis [159] in 1988 (supervised by Bernd Aulbach) in order to unify continuous and discrete analysis. This book is an intro duction to the study of dynamic equations on time scales. Many results concerning differential equations carryover quite easily to corresponding results for difference equations, while other results seem to be completely different in nature from their continuous counterparts. The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice, once for differential equa tions and once for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale, which is an arbitrary nonempty closed subset of the reals.
Book Synopsis Qualitative Theory of Volterra Difference Equations by : Youssef N. Raffoul
Download or read book Qualitative Theory of Volterra Difference Equations written by Youssef N. Raffoul and published by Springer. This book was released on 2018-09-12 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and systematic approach to the study of the qualitative theory of boundedness, periodicity, and stability of Volterra difference equations. The book bridges together the theoretical aspects of Volterra difference equations with its applications to population dynamics. Applications to real-world problems and open-ended problems are included throughout. This book will be of use as a primary reference to researchers and graduate students who are interested in the study of boundedness of solutions, the stability of the zero solution, or in the existence of periodic solutions using Lyapunov functionals and the notion of fixed point theory.
Book Synopsis International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics by :
Download or read book International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics written by and published by . This book was released on 1963 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Partial Differential Equations III by : Michael E. Taylor
Download or read book Partial Differential Equations III written by Michael E. Taylor and published by Springer Science & Business Media. This book was released on 2010-11-02 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is aimed at graduate students in mathematics, and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis
Book Synopsis Half-Linear Differential Equations by : Ondrej Dosly
Download or read book Half-Linear Differential Equations written by Ondrej Dosly and published by Elsevier. This book was released on 2005-07-06 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations.- The first complete treatment of the qualitative theory of half-linear differential equations.- Comparison of linear and half-linear theory.- Systematic approach to half-linear oscillation and asymptotic theory.- Comprehensive bibliography and index.- Useful as a reference book in the topic.
Book Synopsis Mathematics for Economics, fourth edition by : Michael Hoy
Download or read book Mathematics for Economics, fourth edition written by Michael Hoy and published by MIT Press. This book was released on 2022-03-29 with total page 1103 pages. Available in PDF, EPUB and Kindle. Book excerpt: An updated edition of a widely used textbook, offering a clear and comprehensive presentation of mathematics for undergraduate economics students. This text offers a clear and comprehensive presentation of the mathematics required to tackle problems in economic analyses, providing not only straightforward exposition of mathematical methods for economics students at the intermediate and advanced undergraduate levels but also a large collection of problem sets. This updated and expanded fourth edition contains numerous worked examples drawn from a range of important areas, including economic theory, environmental economics, financial economics, public economics, industrial organization, and the history of economic thought. These help students develop modeling skills by showing how the same basic mathematical methods can be applied to a variety of interesting and important issues. The five parts of the text cover fundamentals, calculus, linear algebra, optimization, and dynamics. The only prerequisite is high school algebra; the book presents all the mathematics needed for undergraduate economics. New to this edition are “Reader Assignments,” short questions designed to test students’ understanding before they move on to the next concept. The book’s website offers additional material, including more worked examples (as well as examples from the previous edition). Separate solutions manuals for students and instructors are also available.
Book Synopsis Qualitative Analysis of Set-Valued Differential Equations by : Anatoly A. Martynyuk
Download or read book Qualitative Analysis of Set-Valued Differential Equations written by Anatoly A. Martynyuk and published by Springer. This book was released on 2019-04-02 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness. Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.
Book Synopsis Proceedings of the Conference on Differential & Difference Equations and Applications by : Ravi P. Agarwal
Download or read book Proceedings of the Conference on Differential & Difference Equations and Applications written by Ravi P. Agarwal and published by Hindawi Publishing Corporation. This book was released on 2006 with total page 1266 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Difference Equations, Second Edition by : Ronald E. Mickens
Download or read book Difference Equations, Second Edition written by Ronald E. Mickens and published by CRC Press. This book was released on 2022-02-17 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the study of difference equations has acquired a new significance, due in large part to their use in the formulation and analysis of discrete-time systems, the numerical integration of differential equations by finite-difference schemes, and the study of deterministic chaos. The second edition of Difference Equations: Theory and Applications provides a thorough listing of all major theorems along with proofs. The text treats the case of first-order difference equations in detail, using both analytical and geometrical methods. Both ordinary and partial difference equations are considered, along with a variety of special nonlinear forms for which exact solutions can be determined. Numerous worked examples and problems allow readers to fully understand the material in the text. They also give possible generalization of the theorems and application models. The text's expanded coverage of application helps readers appreciate the benefits of using difference equations in the modeling and analysis of "realistic" problems from a broad range of fields. The second edition presents, analyzes, and discusses a large number of applications from the mathematical, biological, physical, and social sciences. Discussions on perturbation methods and difference equation models of differential equation models of differential equations represent contributions by the author to the research literature. Reference to original literature show how the elementary models of the book can be extended to more realistic situations. Difference Equations, Second Edition gives readers a background in discrete mathematics that many workers in science-oriented industries need as part of their general scientific knowledge. With its minimal mathematical background requirements of general algebra and calculus, this unique volume will be used extensively by students and professional in science and technology, in areas such as applied mathematics, control theory, population science, economics, and electronic circuits, especially discrete signal processing.
