Infinite Interval Problems For Differential Difference And Integral Equations

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Infinite Interval Problems for Differential, Difference and Integral Equations

Author : R.P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 9401007187
Total Pages : 350 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Infinite Interval Problems for Differential, Difference and Integral Equations by : R.P. Agarwal

Download or read book Infinite Interval Problems for Differential, Difference and Integral Equations written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be that until the 1970's for the infinite interval problem all the theoretical results available required rather technical hypotheses and were applicable only to narrowly defined classes of problems. Thus scientists mainly offer~d and used special devices to construct the numerical solution assuming tacitly the existence of a solution. In recent years a mixture of classical analysis and modern fixed point theory has been employed to study the existence of solutions to infinite interval problems. This has resulted in widely applicable results. This monograph is a cumulation mainly of the authors' research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is that we illustrate almost all the results with examples. The plan of this monograph is as follows. In Chapter 1 we present the existence theory for second order boundary value problems on infinite intervals. We begin with several examples which model real world phenom ena. A brief history of the infinite interval problem is also included. We then present general existence results for several different types of boundary value problems. Here we note that for the infinite interval problem only two major approaches are available in the literature.

Positive Solutions of Differential, Difference and Integral Equations

Author : R.P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 9401591717
Total Pages : 425 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Positive Solutions of Differential, Difference and Integral Equations by : R.P. Agarwal

Download or read book Positive Solutions of Differential, Difference and Integral Equations written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: In analysing nonlinear phenomena many mathematical models give rise to problems for which only nonnegative solutions make sense. In the last few years this discipline has grown dramatically. This state-of-the-art volume offers the authors' recent work, reflecting some of the major advances in the field as well as the diversity of the subject. Audience: This volume will be of interest to graduate students and researchers in mathematical analysis and its applications, whose work involves ordinary differential equations, finite differences and integral equations.

Asymptotic Behavior of Solutions of Differential-Difference Equations

Author : Richard Bellman
Publisher : American Mathematical Soc.
ISBN 13 : 0821812351
Total Pages : 99 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Asymptotic Behavior of Solutions of Differential-Difference Equations by : Richard Bellman

Download or read book Asymptotic Behavior of Solutions of Differential-Difference Equations written by Richard Bellman and published by American Mathematical Soc.. This book was released on 1959 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Differential and Difference Equations with Applications

Author : Sandra Pinelas
Publisher : Springer Nature
ISBN 13 : 3030563235
Total Pages : 754 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Differential and Difference Equations with Applications by : Sandra Pinelas

Download or read book Differential and Difference Equations with Applications written by Sandra Pinelas and published by Springer Nature. This book was released on 2020-10-21 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019. First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.

Singular Differential and Integral Equations with Applications

Author : R.P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 9401730040
Total Pages : 412 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Singular Differential and Integral Equations with Applications by : R.P. Agarwal

Download or read book Singular Differential and Integral Equations with Applications written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last century many problems which arose in the science, engineer ing and technology literature involved nonlinear complex phenomena. In many situations these natural phenomena give rise to (i). ordinary differ ential equations which are singular in the independent and/or dependent variables together with initial and boundary conditions, and (ii). Volterra and Fredholm type integral equations. As one might expect general exis tence results were difficult to establish for the problems which arose. Indeed until the early 1990's only very special examples were examined and these examples were usually tackled using some special device, which was usually only applicable to the particular problem under investigation. However in the 1990's new results in inequality and fixed point theory were used to present a very general existence theory for singular problems. This mono graph presents an up to date account of the literature on singular problems. One of our aims also is to present recent theory on singular differential and integral equations to a new and wider audience. The book presents a compact, thorough, and self-contained account for singular problems. An important feature of this book is that we illustrate how easily the theory can be applied to discuss many real world examples of current interest. In Chapter 1 we study differential equations which are singular in the independent variable. We begin with some standard notation in Section 1. 2 and introduce LP-Caratheodory functions. Some fixed point theorems, the Arzela- Ascoli theorem and Banach's theorem are also stated here.

Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains

Download Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains PDF Online Free

Author : Feliz Manuel Minhos
Publisher : World Scientific
ISBN 13 : 9811225141
Total Pages : 243 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains by : Feliz Manuel Minhos

Download or read book Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains written by Feliz Manuel Minhos and published by World Scientific. This book was released on 2022-04-11 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap. The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically. The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'ski? fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Carathéodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity. Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.

Method of Averaging for Differential Equations on an Infinite Interval

Author : Vladimir Burd
Publisher : CRC Press
ISBN 13 : 9781584888758
Total Pages : 360 pages
Book Rating : 4.8/5 (887 download)

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Book Synopsis Method of Averaging for Differential Equations on an Infinite Interval by : Vladimir Burd

Download or read book Method of Averaging for Differential Equations on an Infinite Interval written by Vladimir Burd and published by CRC Press. This book was released on 2007-03-19 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications. Encompassing these novel aspects, Method of Averaging of the Infinite Interval: Theory and Applications rigorously explains the modern theory of the method of averaging and provides a solid understanding of the results obtained when applying this theory. The book starts with the less complicated theory of averaging linear differential equations (LDEs), focusing on almost periodic functions. It describes stability theory and Shtokalo's method, and examines various applications, including parametric resonance and the construction of asymptotics. After establishing this foundation, the author goes on to explore nonlinear equations. He studies standard form systems in which the right-hand side of a system is proportional to a small parameter and proves theorems similar to Banfi's theorem. The final chapters are devoted to systems with a rapidly rotating phase. Covering an important asymptotic method of differential equations, this book provides a thorough understanding of the method of averaging theory and its resulting applications.

Boundary Value Problems From Higher Order Differential Equations

Author : Ravi P Agarwal
Publisher : World Scientific
ISBN 13 : 9814513636
Total Pages : 321 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Boundary Value Problems From Higher Order Differential Equations by : Ravi P Agarwal

Download or read book Boundary Value Problems From Higher Order Differential Equations written by Ravi P Agarwal and published by World Scientific. This book was released on 1986-07-01 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Some ExamplesLinear ProblemsGreen's FunctionMethod of Complementary FunctionsMethod of AdjointsMethod of ChasingSecond Order EquationsError Estimates in Polynomial InterpolationExistence and UniquenessPicard's and Approximate Picard's MethodQuasilinearization and Approximate QuasilinearizationBest Possible Results: Weight Function TechniqueBest Possible Results: Shooting MethodsMonotone Convergence and Further ExistenceUniqueness Implies ExistenceCompactness Condition and Generalized SolutionsUniqueness Implies UniquenessBoundary Value FunctionsTopological MethodsBest Possible Results: Control Theory MethodsMatching MethodsMaximal SolutionsMaximum PrincipleInfinite Interval ProblemsEquations with Deviating Arguments Readership: Graduate students, numerical analysts as well as researchers who are studying open problems. Keywords:Boundary Value Problems;Ordinary Differential Equations;Green's Function;Quasilinearization;Shooting Methods;Maximal Solutions;Infinite Interval Problems

An Introduction to Ordinary Differential Equations

Author : Ravi P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 0387712763
Total Pages : 333 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis An Introduction to Ordinary Differential Equations by : Ravi P. Agarwal

Download or read book An Introduction to Ordinary Differential Equations written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.

Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices

Author : Simon N. Chandler-Wilde
Publisher : American Mathematical Soc.
ISBN 13 : 0821852434
Total Pages : 126 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices by : Simon N. Chandler-Wilde

Download or read book Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices written by Simon N. Chandler-Wilde and published by American Mathematical Soc.. This book was released on 2011 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first half of this memoir the authors explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). They build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator $A$ (its operator spectrum). In the second half of this memoir the authors study bounded linear operators on the generalised sequence space $\ell^p(\mathbb{Z}^N,U)$, where $p\in [1,\infty]$ and $U$ is some complex Banach space. They make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator $A$ is a locally compact perturbation of the identity. Especially, they obtain stronger results than previously known for the subtle limiting cases of $p=1$ and $\infty$.

Advanced Differential Equations

Author : Youssef N. Raffoul
Publisher : Academic Press
ISBN 13 : 0323992811
Total Pages : 366 pages
Book Rating : 4.3/5 (239 download)

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Book Synopsis Advanced Differential Equations by : Youssef N. Raffoul

Download or read book Advanced Differential Equations written by Youssef N. Raffoul and published by Academic Press. This book was released on 2022-04-13 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Differential Equations provides coverage of high-level topics in ordinary differential equations and dynamical systems. The book delivers difficult material in an accessible manner, utilizing easier, friendlier notations and multiple examples. Sections focus on standard topics such as existence and uniqueness for scalar and systems of differential equations, the dynamics of systems, including stability, with examples and an examination of the eigenvalues of an accompanying linear matrix, as well as coverage of existing literature. From the eigenvalues' approach, to coverage of the Lyapunov direct method, this book readily supports the study of stable and unstable manifolds and bifurcations. Additional sections cover the study of delay differential equations, extending from ordinary differential equations through the extension of Lyapunov functions to Lyapunov functionals. In this final section, the text explores fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations. Includes content from a class-tested over multiple years with advanced undergraduate and graduate courses Presents difficult material in an accessible manner by utilizing easier, friendlier notations, multiple examples and thoughtful exercises of increasing difficulty Provides content that is appropriate for advanced classes up to, and including, a two-semester graduate course in exploring the theory and applications of ordinary differential equations Requires minimal background in real analysis and differential equations Offers a partial solutions manual for student study

Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities

Author : Bashir Ahmad
Publisher : Springer
ISBN 13 : 3319521411
Total Pages : 414 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities by : Bashir Ahmad

Download or read book Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities written by Bashir Ahmad and published by Springer. This book was released on 2017-03-16 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.

Ordinary and Partial Differential Equations

Author : Ravi P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 0387791469
Total Pages : 422 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Ordinary and Partial Differential Equations by : Ravi P. Agarwal

Download or read book Ordinary and Partial Differential Equations written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2008-11-13 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.

Differential Equations, Chaos and Variational Problems

Author : Vasile Staicu
Publisher : Springer Science & Business Media
ISBN 13 : 3764384824
Total Pages : 435 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Differential Equations, Chaos and Variational Problems by : Vasile Staicu

Download or read book Differential Equations, Chaos and Variational Problems written by Vasile Staicu and published by Springer Science & Business Media. This book was released on 2008-03-12 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.

Exact and Truncated Difference Schemes for Boundary Value ODEs

Author : Ivan Gavrilyuk
Publisher : Springer Science & Business Media
ISBN 13 : 3034801076
Total Pages : 247 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Exact and Truncated Difference Schemes for Boundary Value ODEs by : Ivan Gavrilyuk

Download or read book Exact and Truncated Difference Schemes for Boundary Value ODEs written by Ivan Gavrilyuk and published by Springer Science & Business Media. This book was released on 2011-08-12 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in this book can be considered as further developments of the results presented in the highly respected books of the Russian mathematician A. A. Samarskii. It is shown that the new Samarskii-like techniques open the horizon for the numerical treatment of more complicated problems. The book contains exercises and the corresponding solutions enabling the use as a course text or for self-study. Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving boundary value ODEs.

Topological Methods in the Study of Boundary Value Problems

Author : Pablo Amster
Publisher : Springer Science & Business Media
ISBN 13 : 1461488931
Total Pages : 226 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Topological Methods in the Study of Boundary Value Problems by : Pablo Amster

Download or read book Topological Methods in the Study of Boundary Value Problems written by Pablo Amster and published by Springer Science & Business Media. This book was released on 2013-10-23 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of general analysis is needed, making the book understandable to non-specialists. The main topics in the study of boundary value problems are present in this text, so readers with some experience in functional analysis or differential equations may also find some elements that complement and enrich their tools for solving nonlinear problems. In comparison with other texts in the field, this one has the advantage of a concise and informal style, thus allowing graduate and undergraduate students to enjoy some of the beauties of this interesting branch of mathematics. Exercises and examples are included throughout the book, providing motivation for the reader.

Algorithms as a Basis of Modern Applied Mathematics

Author : Šárka Hošková-Mayerová
Publisher : Springer Nature
ISBN 13 : 3030613348
Total Pages : 515 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Algorithms as a Basis of Modern Applied Mathematics by : Šárka Hošková-Mayerová

Download or read book Algorithms as a Basis of Modern Applied Mathematics written by Šárka Hošková-Mayerová and published by Springer Nature. This book was released on 2021-01-13 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a self-contained guide to advanced algorithms and their applications in various fields of science. Gathering contributions by authoritative researchers in the field of mathematics, statistics and computer science, it aims at offering a comprehensive and up-to-date view of algorithms, including the theory behind them, as well as practical considerations, current limitations and solutions. It covers applications in energy management, decision making, computer networks, materials science, mechanics and process optimization. It offers an integrated and timely guide to important algorithms, and represents a valuable reference resource for graduate students and researchers in various fields of applied mathematics, statistics and engineering.