Inequalities For Differential And Integral Equations

Author : Anonim
Publisher : Elsevier
Page : 623 pages
File Size : 43,5 Mb
Release : 1997-11-12
Category : Mathematics
ISBN : 9780080534640

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Inequalities for Differential and Integral Equations by Anonim Pdf

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course. Covers a variety of linear and nonlinear inequalities which find widespread applications in the theory of various classes of differential and integral equations Contains many inequalities which have only recently appeared in literature and cannot yet be found in other books Provides a valuable reference to engineers and graduate students

Author : V. Lakshmikantham,S. Leela
Publisher : Academic Press
Page : 389 pages
File Size : 50,8 Mb
Release : 1969
Category : Computers
ISBN : 9780080955636

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Differential and Integral Inequalities: Theory and Applications by V. Lakshmikantham,S. Leela Pdf

This volume constitutes the first part of a monograph on theory and applications of differential and integral inequalities. 'The entire work, as a whole, is intended to be a research monograph, a guide to the literature, and a textbook for advanced courses. The unifying theme of this treatment is a systematic development of the theory and applications of differential inequalities as well as Volterra integral inequalities. The main tools for applications are the norm and the Lyapunov functions. Familiarity with real and complex analysis, elements of general topology and functional analysis, and differential and integral equations is assumed.

Author : Wolfgang Walter
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642864056

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Differential and Integral Inequalities by Wolfgang Walter Pdf

In 1964 the author's mono graph "Differential- und Integral-Un gleichungen," with the subtitle "und ihre Anwendung bei Abschätzungs und Eindeutigkeitsproblemen" was published. The present volume grew out of the response to the demand for an English translation of this book. In the meantime the literature on differential and integral in equalities increased greatly. We have tried to incorporate new results as far as possible. As a matter of fact, the Bibliography has been almost doubled in size. The most substantial additions are in the field of existence theory. In Chapter I we have included the basic theorems on Volterra integral equations in Banach space (covering the case of ordinary differential equations in Banach space). Corresponding theorems on differential inequalities have been added in Chapter II. This was done with a view to the new sections; dealing with the line method, in the chapter on parabolic differential equations. Section 35 contains an exposition of this method in connection with estimation and convergence. An existence theory for the general nonlinear parabolic equation in one space variable based on the line method is given in Section 36. This theory is considered by the author as one of the most significant recent applications of in equality methods. We should mention that an exposition of Krzyzanski's method for solving the Cauchy problem has also been added. The numerous requests that the new edition include a chapter on elliptic differential equations have been satisfied to some extent.

Author : Yuming Qin
Publisher : Birkhäuser
Page : 989 pages
File Size : 49,9 Mb
Release : 2016-10-08
Category : Mathematics
ISBN : 9783319333014

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Integral and Discrete Inequalities and Their Applications by Yuming Qin Pdf

This book focuses on one- and multi-dimensional linear integral and discrete Gronwall-Bellman type inequalities. It provides a useful collection and systematic presentation of known and new results, as well as many applications to differential (ODE and PDE), difference, and integral equations. With this work the author fills a gap in the literature on inequalities, offering an ideal source for researchers in these topics. The present volume is part 1 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.

Author : D.D. Bainov,P.S Simeonov
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 54,7 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401580342

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Integral Inequalities and Applications by D.D. Bainov,P.S Simeonov Pdf

This volume is devoted to integral inequalities of the Gronwall-Bellman-Bihari type. Following a systematic exposition of linear and nonlinear inequalities, attention is paid to analogues including integro-differential inequalities, functional differential inequalities, and discrete and abstract analogues. Applications to the investigation of the properties of solutions of various classes of equations such as uniqueness, stability, dichotomy, asymptotic equivalence and behaviour is also discussed. The book comprises three chapters. Chapter I and II consider classical linear and nonlinear integral inequalities. Chapter III is devoted to various classes of integral inequalities of Gronwall type, and their analogues, which find applications in the theory of integro-differential equations, partial differential equations, differential equations with deviating argument, impube differential equations, etc. Each chapter concludes with a section illustrating the manner of application. The book also contains an extensive bibliography. For researchers whose work involves the theory and application of integral inequalities in mathematics, engineering and physics.

Author : Lakshmikantham
Publisher : Academic Press
Page : 316 pages
File Size : 49,9 Mb
Release : 1969
Category : Computers
ISBN : 9780080955643

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Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations by Lakshmikantham Pdf

Differential and integral inequalities; theory and applications PART B: Functional, partial, abstract, and complex differential equations

Author : Dragoslav S. Mitrinovic,J. Pecaric,A.M Fink
Publisher : Springer Science & Business Media
Page : 606 pages
File Size : 43,5 Mb
Release : 1991-07-31
Category : Mathematics
ISBN : 0792313305

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Inequalities Involving Functions and Their Integrals and Derivatives by Dragoslav S. Mitrinovic,J. Pecaric,A.M Fink Pdf

This volume provides a comprehensive, up-to-date survey of inequalities that involve a relationship between a function and its derivatives or integrals. The book is divided into 18 chapters, some of which are devoted to specific inequalities such as those of Kolmogorov-Landau, Wirtinger, Hardy, Carlson, Hilbert, Caplygin, Lyapunov, Gronwell and others. Over 800 references to the literature are cited; proofs are given when these provide insight into the general methods involved; and applications, especially to the theory of differential equations, are mentioned when appropriate. This volume will interest all those whose work involves differential and integral equations. It can also be recommended as a supplementary text.

Author : Yuming Qin
Publisher : Birkhäuser
Page : 1072 pages
File Size : 40,6 Mb
Release : 2016-10-06
Category : Mathematics
ISBN : 9783319333045

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Integral and Discrete Inequalities and Their Applications by Yuming Qin Pdf

This book concentrates on one- and multi-dimensional nonlinear integral and discrete Gronwall-Bellman type inequalities. It complements the author’s book on linear inequalities and serves as an essential tool for researchers interested in differential (ODE and PDE), difference, and integral equations. The present volume is part 2 of the author’s two-volume work on inequalities. Integral and discrete inequalities are a very important tool in classical analysis and play a crucial role in establishing the well-posedness of the related equations, i.e., differential, difference and integral equations.

Author : C. Corduneanu
Publisher : American Mathematical Soc.
Page : 205 pages
File Size : 50,6 Mb
Release : 2008-05-09
Category : Mathematics
ISBN : 9780821846223

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Principles of Differential and Integral Equations by C. Corduneanu Pdf

In summary, the author has provided an elegant introduction to important topics in the theory of ordinary differential equations and integral equations. -- Mathematical Reviews This book is intended for a one-semester course in differential and integral equations for advanced undergraduates or beginning graduate students, with a view toward preparing the reader for graduate-level courses on more advanced topics. There is some emphasis on existence, uniqueness, and the qualitative behavior of solutions. Students from applied mathematics, physics, and engineering will find much of value in this book. The first five chapters cover ordinary differential equations. Chapter 5 contains a good treatment of the stability of ODEs. The next four chapters cover integral equations, including applications to second-order differential equations. Chapter 7 is a concise introduction to the important Fredholm theory of linear integral equations. The final chapter is a well-selected collection of fascinating miscellaneous facts about differential and integral equations. The prerequisites are a good course in advanced calculus, some preparation in linear algebra, and a reasonable acquaintance with elementary complex analysis. There are exercises throughout the text, with the more advanced of them providing good challenges to the student.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 41,7 Mb
Release : 1969
Category : Differential equations
ISBN : OCLC:472220045

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Differential and Integral Inequalities by Anonim Pdf

Author : Ravi P. Agarwal,Shusen Ding,Craig Nolder
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 50,7 Mb
Release : 2009-09-19
Category : Mathematics
ISBN : 9780387684178

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Inequalities for Differential Forms by Ravi P. Agarwal,Shusen Ding,Craig Nolder Pdf

This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.

Author : B.G. Pachpatte
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 52,7 Mb
Release : 2011-07-26
Category : Mathematics
ISBN : 9789491216176

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Multidimensional Integral Equations and Inequalities by B.G. Pachpatte Pdf

Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.

Author : V. Lakshmikantham,S. Leela
Publisher : Unknown
Page : 390 pages
File Size : 54,8 Mb
Release : 1969
Category : Calculus, Integral
ISBN : 0124341012

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Differential and Integral Inequalities by V. Lakshmikantham,S. Leela Pdf

Author : Dorin Andrica,Themistocles M. Rassias
Publisher : Springer Nature
Page : 848 pages
File Size : 43,8 Mb
Release : 2019-11-14
Category : Mathematics
ISBN : 9783030274078

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Differential and Integral Inequalities by Dorin Andrica,Themistocles M. Rassias Pdf

Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.

Author : B. G. Pachpatte
Publisher : Elsevier
Page : 320 pages
File Size : 51,8 Mb
Release : 2006-09-14
Category : Mathematics
ISBN : 0080464793

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Integral and Finite Difference Inequalities and Applications by B. G. Pachpatte Pdf

The monograph is written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. It contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools and will be a valuable source for a long time to come. It is self-contained and thus should be useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies. Contains a variety of inequalities discovered which find numerous applications in various branches of differential, integral and finite difference equations Valuable reference for someone requiring results about inequalities for use in some applications in various other branches of mathematics Highlights pure and applied mathematics and other areas of science and technology