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Stability Analysis of Nonlinear Systems
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Theory Of Impulsive Differential Equations
Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly. These processes are subject to short-term perturbations whose duration is negligible in comparison with the duration of the process. Consequently, it is natural to assume that these perturbations act instantaneously, that is, in the form of impulses. It is known, for example, that many biological phenomena involving thresholds, bursting rhythm models in medicine and biology, optimal control models in economics, pharmacokinetics and frequency modulated systems, do exhibit impulsive effects. Thus impulsive differential equations, that is, differential equations involving impulse effects, appear as a natural description of observed evolution phenomena of several real world problems.
Inequalities and Applications 2010
Inequalities arise as an essential component in various mathematical areas. Besides forming a highly important collection of tools, e.g. for proving analytic or stochastic theorems or for deriving error estimates in numerical mathematics, they constitute a challenging research field of their own. Inequalities also appear directly in mathematical models for applications in science, engineering, and economics. This edited volume covers divers aspects of this fascinating field. It addresses classical inequalities related to means or to convexity as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities ...
Uniqueness And Nonuniqueness Criteria For Ordinary Differential Equations
This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.
Stability Analysis In Terms Of Two Measures
The problems of modern society are both complex and multidisciplinary. In spite of the apparent diversity of problems, tools developed in one context are often adaptable to an entirely different situation. The concepts of Lyapunov stability have given rise to many new notions that are important in applications. Relative to each concept, there exists a sufficient literature parallel to Lyapunov's theory of stability. It is natural to ask whether we can find a notion and develop the corresponding theory which unifies and includes a variety of known concepts of stability in a single set up. The answer is yes and it is the development of stability theory in terms of two measures. It is in this spirit the authors see the importance of the present monograph. Its aim is to present a systematic account of recent developments in the stability theory in terms of two distinct measures, describe the current state of the art, show the essential unity achieved by wealth of applications, and provide a unified general structure applicable to several nonlinear problems.
Practical Stability Of Nonlinear Systems
This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.
