Integral and Discrete Inequalities and Their Applications
Integral and Discrete Inequalities and Their Applications

Author: Yuming Qin

Publisher: Birkhäuser

Published: 2016-10-06

Total Pages: 1083

ISBN-13: 3319333046

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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.

Integral Inequalities and Applications
Integral Inequalities and Applications

Author: D.D. Bainov

Publisher: Springer Science & Business Media

Published: 2013-04-18

Total Pages: 254

ISBN-13: 9401580340

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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.

Differential and Integral Inequalities
Differential and Integral Inequalities

Author: Dorin Andrica

Publisher: Springer Nature

Published: 2019-11-14

Total Pages: 848

ISBN-13: 3030274071

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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.

Integral and Discrete Inequalities and Their Applications
Integral and Discrete Inequalities and Their Applications

Author: Yuming Qin

Publisher: Birkhäuser

Published: 2016-10-08

Total Pages: 1000

ISBN-13: 3319333011

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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.

Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis
Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis

Author: Changpin Li

Publisher: World Scientific

Published: 2013

Total Pages: 414

ISBN-13: 9814436461

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Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation.Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed.In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc.In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications.

Some Gronwall Type Inequalities and Applications
Some Gronwall Type Inequalities and Applications

Author: Sever Silvestru Dragomir

Publisher:

Published: 2003

Total Pages: 210

ISBN-13:

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Gronwall type integral inequalities of one variable for real functions play a very important role in the Qualitative Theory of Differential Equations. The main aim of the present research monograph is to present some natural applications of Gronwall inequalities with non-linear kernels of Lipschitz type of the problems of boundedness and convergence to zero at infinity of the solutions of certain Volterra integral equations. Stability, uniform stability, uniform asymptotic stability and global asymptotic stability properties for trivial solution of certain differential system of equations are also investigated. Contents: Preface; Integral Inequalities of Gronwall Type; Inequalities for Kernels of (L)-Type; Applications to Integral Equations; Applications to Differential Equations; Index.

Inequalities Involving Functions and Their Integrals and Derivatives
Inequalities Involving Functions and Their Integrals and Derivatives

Author: Dragoslav S. Mitrinovic

Publisher: Springer Science & Business Media

Published: 1991-07-31

Total Pages: 606

ISBN-13: 9780792313304

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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.

Inequalities for Finite Difference Equations
Inequalities for Finite Difference Equations

Author: B.G. Pachpatte

Publisher: CRC Press

Published: 2001-12-13

Total Pages: 546

ISBN-13: 9780824706579

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"A treatise on finite difference ineuqalities that have important applications to theories of various classes of finite difference and sum-difference equations, including several linear and nonlinear finite difference inequalities appearing for the first time in book form."

Methods in Nonlinear Integral Equations
Methods in Nonlinear Integral Equations

Author: R Precup

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 221

ISBN-13: 9401599866

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Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.