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60 produkter

Differential and Integral Inequalities: Theory and Applications
Volume I: Ordinary Differential Equations
AvS. Leela,V. Lakshmikantham
E-bok
PDF, Engelska, 1969
1 197 kr
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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 applicationsof 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.
Theory of Fuzzy Differential Equations and Inclusions
AvV. Lakshmikantham,Ram N. Mohapatra
Häftad, Engelska, 2019
1 024 kr
Skickas inom 10-15 vardagar
Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a timely introduction to the subject that describes the current state of the theory of fuzzy differential equations and inclusions and provides a systematic account of recent developments. The chapters are presented in a clear and logical way and include the preliminary material for fuzzy set theory; a description of calculus for fuzzy functions, an investigation of the basic theory of fuzzy differential equations, and an introduction to fuzzy differential inclusions.
Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations
AvV. Lakshmikantham,S. Koksal
Häftad, Engelska, 2019
1 024 kr
Skickas inom 10-15 vardagar
A monotone iterative technique is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type. This volume describes that technique, which has played a valuable role in unifying a variety of nonlinear problems, particularly when combined with the quasilinearization method. The first part of this monograph describes the general methodology using the classic approach, while the second part develops the same basic ideas via the variational technique. The text provides a useful and timely reference for applied scientists, engineers and numerical analysts.
Method of Variation of Parameters for Dynamic Systems
AvV. Lakshmikantham,S G Deo
Häftad, Engelska, 2019
1 024 kr
Skickas inom 10-15 vardagar
Method of Variation of Parameters for Dynamic Systems presents a systematic and unified theory of the development of the theory of the method of variation of parameters, its unification with Lyapunov's method and typical applications of these methods. No other attempt has been made to bring all the available literature into one volume. This book is a clear exposition of this important topic in control theory, which is not covered by any other text. Such an exposition finally enables the comparison and contrast of the theory and the applications, thus facilitating further development in this fascinating field.
Handbook of Stochastic Analysis and Applications
AvD. Kannan,V. Lakshmikantham
Häftad, Engelska, 2020
780 kr
Skickas inom 10-15 vardagar
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Theory of Fuzzy Differential Equations and Inclusions
AvV. Lakshmikantham,Ram N. Mohapatra
Inbunden, Engelska, 2003
2 098 kr
Skickas inom 10-15 vardagar
Fuzzy differential functions are applicable to real-world problems in engineering, computer science, and social science. That relevance makes for rapid development of new ideas and theories. This volume is a timely introduction to the subject that describes the current state of the theory of fuzzy differential equations and inclusions and provides a systematic account of recent developments. The chapters are presented in a clear and logical way and include the preliminary material for fuzzy set theory; a description of calculus for fuzzy functions, an investigation of the basic theory of fuzzy differential equations, and an introduction to fuzzy differential inclusions.
Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations
AvV. Lakshmikantham,S. Koksal
Inbunden, Engelska, 2003
3 015 kr
Skickas inom 10-15 vardagar
A monotone iterative technique is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type. This volume describes that technique, which has played a valuable role in unifying a variety of nonlinear problems, particularly when combined with the quasilinearization method. The first part of this monograph describes the general methodology using the classic approach, while the second part develops the same basic ideas via the variational technique. The text provides a useful and timely reference for applied scientists, engineers and numerical analysts.
Origins of Mathematics
AvV. Lakshmikantham,S. Leela
Häftad, Engelska, 2000
704 kr
Skickas inom 10-15 vardagar
Casting aside the usual Eurocentric theories about the origins of mathematics, the authors investigate Vedic texts which originated in ancient India. Aryabhatta, Sulvastrus, and Bhaskaracharya are among the Sanskrit-speaking theoreticians, whose astronomical works contributed to the ancient body of mathematics, preceding the Greeks. This book deals with some of the chronological difficulties in tracing the history of mathematics, as well as the reasons for the decay in the ancient Vedic civilization.
Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems
AvV. Lakshmikantham,V.M. Matrosovm. fl.
Inbunden, Engelska, 1991
1 667 kr
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One service mathematics has rendered the 'Et moi, "', si j'avait su comment en revenir, je n'y serais point all".' human race. It has put common sense back where it belongs, on the topmost shelf next Jules Verne to the dusty canister labelled 'discarded non- sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com- puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Theory of Differential Equations with Unbounded Delay
AvV. Lakshmikantham,Lizhi Wenm. fl.
Inbunden, Engelska, 1994
1 113 kr
Skickas inom 10-15 vardagar
Because the theory of equations with delay terms occurs in a variety of contexts, it is important to provide a framework, whenever possible, to handle as many cases as possible simultaneously so as to bring out a better insight and understanding of the subtle differences of the various equations with delays. Furthermore, such a unified theory would avoid duplication and expose open questions that are significant for future research. It is in this spirit that the authors view the importance of their monograph, which presents a systematic and unified theory of recent developments of equations with unbounded delay, describes the current state of the theory showing the essential unity achieved, and provides a general structure applicable to a variety of problems. It is the first book that: (i) presents a unified framework to investigate the basic existence theory for a variety of equations with delay; (ii) treats the classification of equations with memory precisely so as to bring out the subtle differences between them; (iii) develops a systematic study of stability theory in terms of two different measures which includes several known concepts; and (iv) exhibits the advantages of employing Lyapunov functions on product spaces as well as the method of perturbing Lyapunov functions. This book will be of value to researchers and advanced graduate students in mathematics, electrical engineering and biomathematics.
Dynamic Systems on Measure Chains
AvV. Lakshmikantham,S. Sivasundaramm. fl.
Inbunden, Engelska, 1996
1 666 kr
Skickas inom 10-15 vardagar
From a modelling point of view, it is realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time-scale or measure chain. TTherefore the question can be asked as to whether it is possible to provide a framework which permits handling of both dynamic systems simultaneously so that one can get some insight and a better understanding of the subtle differences of these two different systems. The answer is affirmative, and recently developed theory of dynamic systems on time scales offers the desired unified approach. This book presents the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on time scales. In chapter two, we dynamic systems on time scales and prove the basic properties of solutions of such dynamic systemsare introduced. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup.Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. Some important features of the work are that it demonstrates the interplay of the two different theories, namely, the theory of continuous and discrete dynamic systems, when imbedded in one unified framework and it provides an impetus to investigate in the set p of time scales other important problems which might offer a better understanding of the intricacies of a unified study.
Nonlinear Integral Equations in Abstract Spaces
AvDajun Guo,V. Lakshmikanthamm. fl.
Inbunden, Engelska, 1996
1 113 kr
Skickas inom 10-15 vardagar
Many problems arising in the physical sciences, engineering, biology and ap plied mathematics lead to mathematical models described by nonlinear integral equations in abstract spaces. The theory of nonlinear integral equations in ab stract spaces is a fast growing field with important applications to a number of areas of analysis as well as other branches of science. This book is devoted to a comprehensive treatment of nonlinear integral equations in abstract spaces. It is the first book that is dedicated to a systematic development of this subject, and it includes the developments during recent years. Chapter 1 introduces some basic results in analysis, which will be used in later chapters. Chapter 2, which is a main portion of this book, deals with nonlin ear integral equations in Banach spaces, including equations of Fredholm type, of Volterra type and equations of Hammerstein type. Some applica equations tions to nonlinear differential equations in Banach spaces are given. We also discuss an integral equation modelling infectious disease as a typical applica tion. In Chapter 3, we investigate the first order and second order nonlinear integro-differential equations in Banach spaces including equations of Volterra type and equations of mixed type. Chapter 4 is devoted to nonlinear impulsive integral equations in Banach spaces and their applications to nonlinear impul sive differential equations in Banach spaces.
Generalized Quasilinearization for Nonlinear Problems
AvV. Lakshmikantham,A.S. Vatsala
Inbunden, Engelska, 1998
1 667 kr
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The problems of modern society are complex, interdisciplinary and nonlin- ear. ~onlinear problems are therefore abundant in several diverse disciplines. Since explicit analytic solutions of nonlinear problems in terms of familiar, well- trained functions of analysis are rarely possible, one needs to exploit various approximate methods. There do exist a number of powerful procedures for ob- taining approximate solutions of nonlinear problems such as, Newton-Raphson method, Galerkins method, expansion methods, dynamic programming, itera- tive techniques, truncation methods, method of upper and lower bounds and Chapligin method, to name a few. Let us turn to the fruitful idea of Chapligin, see [27] (vol I), for obtaining approximate solutions of a nonlinear differential equation u' = f(t, u), u(O) = uo. Let fl' h be such that the solutions of 1t' = h (t, u), u(O) = uo, and u' = h(t,u), u(O) = uo are comparatively simple to solve, such as linear equations, and lower order equations. Suppose that we have h(t,u) s f(t,u) s h(t,u), for all (t,u).
Handbook of Stochastic Analysis and Applications
AvD. Kannan,V. Lakshmikantham
Inbunden, Engelska, 2001
7 349 kr
Skickas inom 5-8 vardagar
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Trends in Theory and Practice of Nonlinear Differential Equations
AvLakshmikantham Lakshmikantham,V. Lakshmikanthamm. fl.
Häftad, Engelska, 1984
4 160 kr
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This book is based on an International Conference on Trends in Theory and Practice of Nonlinear Differential Equations held at The University of Texas at Arlington. It aims to feature recent trends in theory and practice of nonlinear differential equations.
nonlinear analysis and applications
AvV. Lakshmikantham
Häftad, Engelska, 1987
3 015 kr
Skickas inom 10-15 vardagar
This book attempts to put together the works of a wide range of mathematical scientists. It consists of the proceedings of the Seventh Conference on "Nonlinear Analysis and Applications" including papers that were delivered as invited talks and research reports.
Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations
AvSeppo Heikkila,V. Lakshmikantham
Inbunden, Engelska, 1994
7 454 kr
Skickas inom 10-15 vardagar
"Providing the theoretical framework to model phenomena with discontinuous changes, this unique reference presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations and applies this method to derive suitable fixed point theorems in ordered abstract spaces."
nonlinear analysis and applications
AvV. Lakshmikantham
E-bok
PDF, Engelska, 2020
3 558 kr
Läs direkt efter köp
This book attempts to put together the works of a wide range of mathematical scientists. It consists of the proceedings of the Seventh Conference on "Nonlinear Analysis and Applications" including papers that were delivered as invited talks and research reports.
Trends in Theory and Practice of Nonlinear Differential Equations
AvV. Lakshmikantham
E-bok
PDF, Engelska, 2020
4 913 kr
Läs direkt efter köp
This book is based on an International Conference on Trends in Theory and Practice of Nonlinear Differential Equations held at The University of Texas at Arlington. It aims to feature recent trends in theory and practice of nonlinear differential equations.
nonlinear analysis and applications
AvV. Lakshmikantham
E-bok
Engelska, 2020
3 558 kr
Läs direkt efter köp
This book attempts to put together the works of a wide range of mathematical scientists. It consists of the proceedings of the Seventh Conference on "Nonlinear Analysis and Applications" including papers that were delivered as invited talks and research reports.
Trends in Theory and Practice of Nonlinear Differential Equations
AvV. Lakshmikantham
E-bok
Engelska, 2020
4 913 kr
Läs direkt efter köp
This book is based on an International Conference on Trends in Theory and Practice of Nonlinear Differential Equations held at The University of Texas at Arlington. It aims to feature recent trends in theory and practice of nonlinear differential equations.
Handbook of Stochastic Analysis and Applications
AvV. Lakshmikantham,D. Kannan
E-bok
Engelska, 2001
915 kr
Läs direkt efter köp
An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.
Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations
AvS. Koksal,V. Lakshmikantham
E-bok
Engelska, 2003
1 203 kr
Läs direkt efter köp
A monotone iterative technique is used to obtain monotone approximate solutions that converge to the solution of nonlinear problems of partial differential equations of elliptic, parabolic and hyperbolic type. This volume describes that technique, which has played a valuable role in unifying a variety of nonlinear problems, particularly when combin
Theory Of Difference Equations Numerical Methods And Applications
AvV. Trigiante,V. Lakshmikantham
E-bok
Engelska, 2002
796 kr
Läs direkt efter köp
"Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological polynomials, the Euclidean algorithm, roots of polynomials, and well-conditioning."
Trends in Theory and Practice of Nonlinear Differential Equations
AvV. Lakshmikantham
Inbunden, Engelska, 2017
4 152 kr
Skickas inom 10-15 vardagar
This book is based on an International Conference on Trends in Theory and Practice of Nonlinear Differential Equations held at The University of Texas at Arlington. It aims to feature recent trends in theory and practice of nonlinear differential equations.
Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations
AvV. Lakshmikantham
E-bok
Engelska, 2017
6 098 kr
Läs direkt efter köp
""Providing the theoretical framework to model phenomena with discontinuous changes, this unique reference presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations and applies this method to derive suitable fixed point theorems in ordered abstract spaces.
Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations
AvV. Lakshmikantham
E-bok
PDF, Engelska, 2017
6 035 kr
Läs direkt efter köp
""Providing the theoretical framework to model phenomena with discontinuous changes, this unique reference presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations and applies this method to derive suitable fixed point theorems in ordered abstract spaces.
Method of Variation of Parameters for Dynamic Systems
AvS G Deo,V. Lakshmikantham
E-bok
Engelska, 2019
1 203 kr
Läs direkt efter köp
Method of Variation of Parameters for Dynamic Systems presents a systematic and unified theory of the development of the theory of the method of variation of parameters, its unification with Lyapunov''s method and typical applications of these methods. No other attempt has been made to bring all the available literature into one volume. This book is a clear exposition of this important topic in control theory, which is not covered by any other text. Such an exposition finally enables the comparison and contrast of the theory and the applications, thus facilitating further development in this fascinating field.
Method of Variation of Parameters for Dynamic Systems
AvS G Deo,V. Lakshmikantham
E-bok
PDF, Engelska, 2019
1 191 kr
Läs direkt efter köp
Method of Variation of Parameters for Dynamic Systems presents a systematic and unified theory of the development of the theory of the method of variation of parameters, its unification with Lyapunov''s method and typical applications of these methods. No other attempt has been made to bring all the available literature into one volume. This book is a clear exposition of this important topic in control theory, which is not covered by any other text. Such an exposition finally enables the comparison and contrast of the theory and the applications, thus facilitating further development in this fascinating field.
Dynamic Systems on Measure Chains
AvV. Lakshmikantham,S. Sivasundaramm. fl.
Häftad, Engelska, 2010
1 666 kr
Skickas inom 10-15 vardagar
From a modelling point of view, it is more realistic to model a phenomenon by a dynamic system which incorporates both continuous and discrete times, namely, time as an arbitrary closed set of reals called time-scale or measure chain. It is therefore natural to ask whether it is possible to provide a framework which permits us to handle both dynamic systems simultaneously so that one can get some insight and a better understanding of the subtle differences of these two different systems. The answer is affirmative, and recently developed theory of dynamic systems on time scales offers the desired unified approach. In this monograph, we present the current state of development of the theory of dynamic systems on time scales from a qualitative point of view. It consists of four chapters. Chapter one develops systematically the necessary calculus of functions on time scales. In chapter two, we introduce dynamic systems on time scales and prove the basic properties of solutions of such dynamic systems. The theory of Lyapunov stability is discussed in chapter three in an appropriate setup. Chapter four is devoted to describing several different areas of investigations of dynamic systems on time scales which will provide an exciting prospect and impetus for further advances in this important area which is very new. Some important features of the monograph are as follows: It is the first book that is dedicated to a systematic development of the theory of dynamic systems on time scales which is of recent origin. It demonstrates the interplay of the two different theories, namely, the theory of continuous and discrete dynamic systems, when imbedded in one unified framework. It provides an impetus to investigate in the setup of time scales other important problems which might offer a better understanding of the intricacies of a unified study.£/LIST£ Audience: Thereadership of this book consists of applied mathematicians, engineering scientists, research workers in dynamic systems, chaotic theory and neural nets.

V. Lakshmikantham – författare

Differential and Integral Inequalities: Theory and Applications

Theory of Fuzzy Differential Equations and Inclusions

Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations

Method of Variation of Parameters for Dynamic Systems

Handbook of Stochastic Analysis and Applications

Theory of Fuzzy Differential Equations and Inclusions

Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations

Origins of Mathematics

Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems

Theory of Differential Equations with Unbounded Delay

Dynamic Systems on Measure Chains

Nonlinear Integral Equations in Abstract Spaces

Generalized Quasilinearization for Nonlinear Problems

Handbook of Stochastic Analysis and Applications

Trends in Theory and Practice of Nonlinear Differential Equations

nonlinear analysis and applications

Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations

nonlinear analysis and applications

Trends in Theory and Practice of Nonlinear Differential Equations

nonlinear analysis and applications

Trends in Theory and Practice of Nonlinear Differential Equations

Handbook of Stochastic Analysis and Applications

Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations

Theory Of Difference Equations Numerical Methods And Applications

Trends in Theory and Practice of Nonlinear Differential Equations

Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations

Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations

Method of Variation of Parameters for Dynamic Systems

Method of Variation of Parameters for Dynamic Systems

Dynamic Systems on Measure Chains