Specific Asymptotic Properties Of The Solutions Of Impulsive Differential Equations Methods And Applications
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Impulsive Differential Equations
Author | : Dimit?r Ba?nov |
Publisher | : World Scientific |
Total Pages | : 246 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 9810218230 |
The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations
Author | : Ivan Kiguradze |
Publisher | : Springer Science & Business Media |
Total Pages | : 343 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401118086 |
This volume provides a comprehensive review of the developments which have taken place during the last thirty years concerning the asymptotic properties of solutions of nonautonomous ordinary differential equations. The conditions of oscillation of solutions are established, and some general theorems on the classification of equations according to their oscillatory properties are proved. In addition, the conditions are found under which nonlinear equations do not have singular, proper, oscillatory and monotone solutions. The book has five chapters: Chapter I deals with linear differential equations; Chapter II with quasilinear equations; Chapter III with general nonlinear differential equations; and Chapter IV and V deal, respectively, with higher-order and second-order differential equations of the Emden-Fowler type. Each section contains problems, including some which presently remain unsolved. The volume concludes with an extensive list of references. For researchers and graduate students interested in the qualitative theory of differential equations.
Asymptotic Analysis of Differential Equations
Author | : R. B. White |
Publisher | : World Scientific |
Total Pages | : 430 |
Release | : 2010 |
Genre | : Mathematics |
ISBN | : 1848166087 |
"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Asymptotic Properties of the Solutions of Ordinary Linear Differential Equations Containing a Parameter with Application to Boundary Value and Expansion Problems
Author | : George David Birkhoff |
Publisher | : |
Total Pages | : 48 |
Release | : 1908 |
Genre | : Differential equations, Linear |
ISBN | : |
Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations
Author | : Anatoli? Mikha?lovich Samo?lenko |
Publisher | : World Scientific |
Total Pages | : 323 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 9814329061 |
Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on the random factors. The modern theory of differential equations with random perturbations is on the edge of two mathematical disciplines: random processes and ordinary differential equations. Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations. This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations. For this purpose, both asymptotic and qualitative methods which appeared in the classical theory of differential equations and nonlinear mechanics are developed.
Theory Of Impulsive Differential Equations
Author | : Vangipuram Lakshmikantham |
Publisher | : World Scientific |
Total Pages | : 287 |
Release | : 1989-05-01 |
Genre | : Mathematics |
ISBN | : 9814507261 |
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.
Asymptotic Properties of Oscillatory Solutions of Differential Equations of the N-th Order
Author | : Miroslav BartuĊĦek |
Publisher | : |
Total Pages | : 104 |
Release | : 1992 |
Genre | : Differential equations |
ISBN | : |
Impulsive Differential Equations with a Small Parameter
Author | : Dimit?r Ba?nov |
Publisher | : World Scientific |
Total Pages | : 292 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 9789810214340 |
This book is devoted to impulsive differential equations with a small parameter. It consists of three chapters. Chapter One serves as an introduction. In Chapter Two, regularly perturbed impulsive differential equations are considered. Modifications of the method of small parameter, the averaging method, and the method of integral manifolds are proposed. In Chapter Three, singularly perturbed differential equations are considered. A modification of the method of boundary functions is proposed, and asymptotic expansions along the powers of the small parameters of the solutions of the initial value problem, the periodic problem, and some boundary value problems are found. Numerous nonstandard applications to the theory of optimal control are made. The application of some other methods to impulsive singularly perturbed equations is illustrated, such as the numerical-analytical method for finding periodic solutions, the method of differential inequalities and the averaging method.The book is written clearly, strictly, and understandably. It is intended for mathematicians, physicists, chemists, biologists and economists, as well as for senior students of these specialities.
Asymptotics of Linear Differential Equations
Author | : M.H. Lantsman |
Publisher | : Springer Science & Business Media |
Total Pages | : 450 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 9401597979 |
The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects.