Lyapunov Inequalities And Applications

Author : Ravi P. Agarwal,Martin Bohner,Abdullah Özbekler
Publisher : Springer Nature
Page : 607 pages
File Size : 52,5 Mb
Release : 2021-04-12
Category : Mathematics
ISBN : 9783030690298

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Lyapunov Inequalities and Applications by Ravi P. Agarwal,Martin Bohner,Abdullah Özbekler Pdf

This book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address. This survey starts by introducing basic applications of Lyapunov’s inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems. Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content.

Author : Juan Pablo Pinasco
Publisher : Springer Science & Business Media
Page : 143 pages
File Size : 53,5 Mb
Release : 2013-09-14
Category : Mathematics
ISBN : 9781461485230

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Lyapunov-type Inequalities by Juan Pablo Pinasco Pdf

​The eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequality for quasilinear resonant systems showed the existence of eigenvalue asymptotics driven by the coupling of the equations instead of the order of the equations. For p=2, the coupling and the order of the equations are the same, so this cannot happen in linear problems. Another striking difference between linear and quasilinear second order differential operators is the existence of Lyapunov-type inequalities in R^n when p>n. Since the linear case corresponds to p=2, for the usual Laplacian there exists a Lyapunov inequality only for one-dimensional problems. For linear higher order problems, several Lyapunov-type inequalities were found by Egorov and Kondratiev and collected in On spectral theory of elliptic operators, Birkhauser Basel 1996. However, there exists an interesting interplay between the dimension of the underlying space, the order of the differential operator, the Sobolev space where the operator is defined, and the norm of the weight appearing in the inequality which is not fully developed. Also, the Lyapunov inequality for differential equations in Orlicz spaces can be used to develop an oscillation theory, bypassing the classical sturmian theory which is not known yet for those equations. For more general operators, like the p(x) laplacian, the possibility of existence of Lyapunov-type inequalities remains unexplored. ​

Author : Antonio Cañada,Salvador Villegas
Publisher : Springer
Page : 136 pages
File Size : 45,5 Mb
Release : 2015-11-24
Category : Mathematics
ISBN : 9783319252896

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A Variational Approach to Lyapunov Type Inequalities by Antonio Cañada,Salvador Villegas Pdf

This book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov’s original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and applied mathematics. Originating with the study of the stability properties of the Hill equation, other questions arose for instance in systems at resonance, crystallography, isoperimetric problems, Rayleigh type quotients and oscillation and intervals of disconjugacy and it lead to the study of Lyapunov-type inequalities for differential equations. This classical area of mathematics is still of great interest and remains a source of inspiration.

Author : Vladimir Ivanovich Zubov
Publisher : Unknown
Page : 256 pages
File Size : 47,6 Mb
Release : 1961
Category : Differential equations
ISBN : UVA:X001332811

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Methods of A. M. Lyapunov and Their Application by Vladimir Ivanovich Zubov Pdf

Author : Themistocles RASSIAS
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401143394

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Survey on Classical Inequalities by Themistocles RASSIAS Pdf

Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp -norm inequalities in convolutions, inequalities for polynomial zeros as well as applications in a number of problems of pure and applied mathematics. It is my pleasure to express my appreciation to the distinguished mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staff of Kluwer Academic Publishers. June 2000 Themistocles M. Rassias Vll LYAPUNOV INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA. email address:[email protected] DON B. HINTON Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. email address: [email protected] Abstract. For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential equations as well as Hamiltonian systems. 1. Introduction Lyapunov's inequality has proved useful in the study of spectral properties of ordinary differential equations. Typical applications include bounds for eigenvalues, stability criteria for periodic differential equations, and estimates for intervals of disconjugacy.

Author : Themistocles M. Rassias
Publisher : Springer
Page : 237 pages
File Size : 41,8 Mb
Release : 2011-10-22
Category : Mathematics
ISBN : 9401143404

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Survey on Classical Inequalities by Themistocles M. Rassias Pdf

Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp -norm inequalities in convolutions, inequalities for polynomial zeros as well as applications in a number of problems of pure and applied mathematics. It is my pleasure to express my appreciation to the distinguished mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staff of Kluwer Academic Publishers. June 2000 Themistocles M. Rassias Vll LYAPUNOV INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA. email address:[email protected] DON B. HINTON Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. email address: [email protected] Abstract. For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential equations as well as Hamiltonian systems. 1. Introduction Lyapunov's inequality has proved useful in the study of spectral properties of ordinary differential equations. Typical applications include bounds for eigenvalues, stability criteria for periodic differential equations, and estimates for intervals of disconjugacy.

Author : V. Lakshmikantham,S. Leela
Publisher : Academic Press
Page : 389 pages
File Size : 43,7 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 : Ravi P. Agarwal
Publisher : CRC Press
Page : 1000 pages
File Size : 49,9 Mb
Release : 2000-01-27
Category : Mathematics
ISBN : 9781420027020

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Difference Equations and Inequalities by Ravi P. Agarwal Pdf

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 other disciplines. It features 200 new problems, 400 additional references, and a new chapter on the qualitative properties of solutions of neutral difference equations.

Author : Lakshmikantham
Publisher : Academic Press
Page : 316 pages
File Size : 53,5 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 : Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 50,8 Mb
Release : 2020-08-06
Category : Mathematics
ISBN : 9781119654230

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Fractional Order Analysis by Hemen Dutta,Ahmet Ocak Akdemir,Abdon Atangana Pdf

A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.

Author : Srikanta Patnaik,Vipul Jain
Publisher : Springer
Page : 1267 pages
File Size : 40,5 Mb
Release : 2018-08-22
Category : Technology & Engineering
ISBN : 9789811089442

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Recent Developments in Intelligent Computing, Communication and Devices by Srikanta Patnaik,Vipul Jain Pdf

This book offers a collection of high-quality, peer-reviewed research papers presented at the International Conference on Intelligent Computing, Communication and Devices (ICCD 2017), discussing all dimensions of intelligent sciences – intelligent computing, intelligent communication, and intelligent devices. Intelligent computing addresses areas such as intelligent and distributed computing, intelligent grid and cloud computing, internet of things, soft computing and engineering applications, data mining and knowledge discovery, semantic and web technology, hybrid systems, agent computing, bioinformatics, and recommendation systems. Intelligent communication is concerned with communication and network technologies, such as mobile broadband and all optical networks that are the key to groundbreaking inventions of intelligent communication technologies. It includes communication hardware, software and networked intelligence, mobile technologies, machine-to-machine communication networks, speech and natural language processing, routing techniques and network analytics, wireless ad hoc and sensor networks, communications and information security, signal, image and video processing, network management, and traffic engineering. Lastly, intelligent devices are any equipment, instruments, or machines that have their own computing capability. As computing technology becomes more advanced and less expensive, it can be incorporated an increasing number of devices of all kinds. This area covers such as embedded systems, radiofrequency identification (RFID), radiofrequency microelectromechanical system (RF MEMS), very-large-scale integration (VLSI) design and electronic devices, analog and mixed-signal integrated circuit (IC) design and testing, microelectromechanical system (MEMS) and microsystems, solar cells and photonics, nanodevices, single electron and spintronics devices, space electronics, and intelligent robotics.

Author : Mustafa Inc,Xiao-Jun Yang,Devendra Kumar
Publisher : Frontiers Media SA
Page : 160 pages
File Size : 41,7 Mb
Release : 2023-11-20
Category : Science
ISBN : 9782832539439

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New Numerical and Analytical Methods for Nonlinear Partial Differential Equations with Applications in Quantum Physics by Mustafa Inc,Xiao-Jun Yang,Devendra Kumar Pdf

Various numerical and analytical methods have been used to investigate the models of real-world phenomena. Namely, real-world models from quantum physics have been investigated by many researchers. This Research Topic aims to promote and exchange new and important theoretical and numerical results to study the dynamics of complex physical systems. In particular, the Research Topic will focus on numerical and analytical methods for nonlinear partial differential equations which have applications for quantum physical systems. Authors are encouraged to introduce their latest original research articles. The Research Topic will cover, but is not limited to, the following themes: - Mathematical methods in physics - Representations of Lie groups in physics - Quantum fields - Advanced numerical methods and techniques for nonlinear partial differential equations - Schrödinger classical and fractional operators - Conservation laws

Author : Ondrej Dosly,Pavel Rehak
Publisher : Elsevier
Page : 533 pages
File Size : 43,7 Mb
Release : 2005-07-06
Category : Mathematics
ISBN : 9780080461236

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Half-Linear Differential Equations by Ondrej Dosly,Pavel Rehak Pdf

The book presents a systematic and compact treatment of the qualitative theory of half-linear differential 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.

Author : Laurent El Ghaoui,Silviu-Iulian Niculescu
Publisher : SIAM
Page : 399 pages
File Size : 40,8 Mb
Release : 2000-01-01
Category : Mathematics
ISBN : 0898719836

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Advances in Linear Matrix Inequality Methods in Control by Laurent El Ghaoui,Silviu-Iulian Niculescu Pdf

Linear matrix inequalities (LMIs) have recently emerged as useful tools for solving a number of control problems. This book provides an up-to-date account of the LMI method and covers topics such as recent LMI algorithms, analysis and synthesis issues, nonconvex problems, and applications. It also emphasizes applications of the method to areas other than control.

Author : Dorin Andrica,Themistocles M. Rassias
Publisher : Springer Nature
Page : 848 pages
File Size : 51,6 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.