# krainaksiazek qualitative theory of differential equations 20106996

- znaleziono 23 produkty w 2 sklepach

### Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory Springer, Berlin

**Książki / Literatura obcojęzyczna**

- of nonlinear the of solitons the the last 30 theory partial theory During years - has into solutions of a kind a differential special equations (PDEs) possessing grown and in view the attention of both mathematicians field that attracts physicists large and of the of the problems of its novelty problems. Physical important applications for in the under consideration are mo- to the observed, example, equations leading mathematical discoveries is the Makhankov One of the related V.G. by [60]. graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the inverse called solvable the scattering problem (on subject, are by known nonlinear At the the class of for same time, currently example [89,94]). see, the other there is solvable this method is narrow on hand, PDEs sufficiently and, by of differential The latter called the another qualitative theory equations. approach, the of various in includes on pr- investigations well-posedness approach particular solutions such or lems for these the behavior of as stability blowing-up, equations, these and this of approach dynamical systems generated by equations, etc., properties in wider class of a makes it to an problems (maybe possible investigate essentially more general study).

Sklep: Libristo.pl

### Half-Linear Differential Equations North Holland

**Książki / Literatura obcojęzyczna**

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. This is the first complete treatment of the qualitative theory of half-linear differential equations. This book includes comparison of linear and half-linear theory. It features a systematic approach to half-linear oscillation and asymptotic theory. It contains a comprehensive bibliography and index. It is useful as a reference book in the topic.

Sklep: Libristo.pl

### Ordinary Differential Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations. It additionally develops the basics of control theory, which is a unique feature in current textbook literature.§The following topics are particularly emphasised:§ existence, uniqueness and continuation of solutions,§ continuous dependence on initial data,§ flows,§ qualitative behaviour of solutions,§ limit sets,§ stability theory,§ invariance principles,§ introductory control theory,§ feedback and stabilization.§The last two items cover classical control theoretic material such as linear control theory and absolute stability of nonlinear feedback systems. It also includes an introduction to the more recent concept of input-to-state stability.§Only a basic grounding in linear algebra and analysis is assumed. Ordinary Differential Equations will be suitable for final year undergraduate students of mathematics and appropriate for beginning postgraduates in mathematics and in mathematically oriented engineering and science.§

Sklep: Libristo.pl

### Differential Equations on Complex Manifolds Springer Netherlands

**Książki / Literatura obcojęzyczna**

This volume contains a unique, systematic presentation of the general theory of differential equations on complex manifolds. The six chapters deal with questions concerning qualitative (asymptotic) theory of partial differential equations as well as questions about the existence of solutions in spaces of ramifying functions. Furthermore, much attention is given to applications. In particular, important problems connected with the continuation of (real) solutions to differential equations and with mathematical theory of diffraction are solved here. The book is self-contained, and includes up-to-date results. All necessary terminology is explained. For graduate students and researchers interested in differential equations in partial derivatives, complex analysis, symplectic and contact geometry, integral transformations and operational calculus, and mathematical physics.

Sklep: Libristo.pl

### Functional Differential Equations Springer Netherlands

**Książki / Literatura obcojęzyczna**

This monograph presents the basics of i-smooth calculus, a new differential calculus of nonlinear functionals based on the notion of invariant derivative, and its application to some problems of the qualitative theory of functional differential equations. This book is unique in its separation of finite and infinite dimensional components in the structures of functional differential equations and functionals, as well as in its use of conditional representation of FDEs, which is expedient for the application of methods and constructions of i-smooth calculus. Part I contains a foundation of i-smooth calculus. Part II is an introduction to FDEs based on i-smooth calculus. Part III describes the direct Lyapunov method for systems with delays in terms of i- smooth functionals. Part IV considers an approach to the development of a dynamical programming method for systems with delays in terms of i-smooth Bellman's functionals. Audience: This volume will be of interest to students and researchers in mathematics, applied mathematicians, and engineers whose work involves ordinary differential equations, functional analysis, partial differential equations, optimal control and mathematics systems theory.

Sklep: Libristo.pl

### Applied Functional Differential Equations Wiley

**Książki / Literatura obcojęzyczna**

Features new results and up-to-date advances in modeling and solving differential equations§§Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations.§§The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features:§Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types§Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines§Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay§An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity§An extensive bibliography with over 550 references that connects the presented concepts to further topical exploration§§Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes.

Sklep: Libristo.pl

### Differential Equations: A Dynamical Systems Approach Springer, Berlin

**Książki / Literatura obcojęzyczna**

This corrected third printing retains the authors'main emphasis on ordinary differential equations. It is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. The authors have taken the view that a differential equations theory defines functions; the object of the theory is to understand the behaviour of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods, and the companion software, MacMath, is designed to bring these notions to life.

Sklep: Libristo.pl

### Differential Equations And Dynamical Systems

**Książki Obcojęzyczne>Angielskie>Mathematics & science>Mathematics>Calculus & mathematical analysis>Differential calculus & equationsKsi...**

This Textbook, Ideal For Students And Lecturers Alike, Is A Systematic Study Of The Qualitative And Geometric Theory Of Nonlinear Differential Equations And Dynamical Systems. It Includes A Thorough Treatment Of Linear Systems.

Sklep: Gigant.pl

### Evolution Equations of von Karman Type Springer, Berlin

**Książki / Literatura obcojęzyczna**

In these notes we consider two kinds of nonlinear evolution problems of von Karman type on Euclidean spaces of arbitrary even dimension. Each of these problems consists of a system that results from the coupling of two highly nonlinear partial differential equations, one hyperbolic or parabolic and the other elliptic. These systems take their name from a formal analogy with the von Karman equations in the theory of elasticity in two dimensional space. We establish local (respectively global) results for strong (resp., weak) solutions of these problems and corresponding well-posedness results in the Hadamard sense. Results are found by obtaining regularity estimates on solutions which are limits of a suitable Galerkin approximation scheme. The book is intended as a pedagogical introduction to a number of meaningful application of classical methods in nonlinear Partial Differential Equations of Evolution. The material is self-contained and most proofs are given in full detail.§§The interested reader will gain a deeper insight into the power of nontrivial a priori estimate methods in the qualitative study of nonlinear differential equations.§

Sklep: Libristo.pl

### Delay Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

The aim here is to provide an introduction to the mathematical theory of infinite dimensional dynamical systems by focusing on a relatively simple - yet rich - class of examples, delay differential equations. This textbook contains detailed proofs and many exercises, intended both for self-study and for courses at graduate level, as well as a reference for basic results. As the subtitle indicates, this book is about concepts, ideas, results and methods from linear functional analysis, complex function theory, the qualitative theory of dynamical systems and nonlinear analysis. The book provides the reader with a working knowledge of applied functional analysis and dynamical systems.

Sklep: Libristo.pl

### Global Bifurcation Theory and Hilbert's Sixteenth Problem Springer, Berlin

**Książki / Literatura obcojęzyczna**

On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second Interna tional Congress of Mathematicians in Paris. The talk covered practically all directions of mathematical thought of that time and contained a list of 23 problems which determined the further development of mathema tics in many respects (1, 119]. Hilbert's Sixteenth Problem (the second part) was stated as follows: Problem. To find the maximum number and to determine the relative position of limit cycles of the equation dy Qn(X, y) -= dx Pn(x, y)' where Pn and Qn are polynomials of real variables x, y with real coeffi cients and not greater than n degree. The study of limit cycles is an interesting and very difficult problem of the qualitative theory of differential equations. This theory was origi nated at the end of the nineteenth century in the works of two geniuses of the world science: of the Russian mathematician A. M. Lyapunov and of the French mathematician Henri Poincare. A. M. Lyapunov set forth and solved completely in the very wide class of cases a special problem of the qualitative theory: the problem of motion stability (154]. In turn, H. Poincare stated a general problem of the qualitative analysis which was formulated as follows: not integrating the differential equation and using only the properties of its right-hand sides, to give as more as possi ble complete information on the qualitative behaviour of integral curves defined by this equation (176].

Sklep: Libristo.pl

### Bifurcation Theory Springer, Berlin

**Książki / Literatura obcojęzyczna**

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations.

Sklep: Libristo.pl

### Optimal Control Theory with Economic Applications Elsevier Science & Technology

**Książki / Literatura obcojęzyczna**

This book serves not only as an introduction, but also as an advanced text and reference source in the field of deterministic optimal control systems governed by ordinary differential equations. It also includes an introduction to the classical calculus of variations. An important feature of the book is the inclusion of a large number of examples, in which the theory is applied to a wide variety of economics problems. The presentation of simple models helps illuminate pertinent qualitative and analytic points, useful when confronted with a more complex reality. These models cover: economic growth in both open and closed economies, exploitation of (non-) renewable resources, pollution control, behaviour of firms, and differential games. A great emphasis on precision pervades the book, setting it apart from the bulk of literature in this area. The rigorous techniques presented should help the reader avoid errors which often recur in the application of control theory within economics.

Sklep: Libristo.pl

### Contract Theory in Continuous Time Models Springer, Berlin

**Książki / Literatura obcojęzyczna**

In the recent years there has been a significant increase in the interest in continuous-time Principal-Agent models, or contract theory, and their applications. Continuous-time models provide a powerful and elegant framework for solving stochastic optimization problems of finding the optimal contracts between two parties, under various assumptions on the information they have access to, and the effect they have on the underlying "profit/los" values. This monograph surveys recent results of the theory in a systematic way, using the approach of the so-called Stochastic Maximum Principle, in models driven by Brownian Motion.§Optimal contracts are characterized via a system of Forward-Backward Stochastic Differential Equations. In a number of interesting special cases these can be solved explicitly, enabling derivation of many qualitative economic conclusions.

Sklep: Libristo.pl

### Generalized Inverse Operators and Fredholm Boundary-value Problems VSP International Science Publishers

**Książki / Literatura obcojęzyczna**

The problems of development of constructive methods for the analysis of linear and weakly nonlinear boundary-value problems for a broad class of functional differential equations traditionally occupy one of the central places in the qualitative theory of differential equations.The authors of this monograph suggest some methods for the construction of the generalized inverse (or pseudo-inverse) operators for the original linear Fredholm operators in Banach (or Hilbert) spaces for boundary-value problems regarded as operator systems in abstract spaces. They also study basic properties of the generalized Green's operator.In the first three chapters some results from the theory of generalized inversion of bounded linear operators in abstract spaces are given, which are then used for the investigation of boundary-value problems for systems of functional differential equations. Subsequent chapters deal with a unified procedure for the investigation of Fredholm boundary-value problems for operator equations; analysis of boundary-value problems for standard operator systems; and existence of solutions of linear and nonlinear differential and difference systems bounded on the entire axis.

Sklep: Libristo.pl

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t1=0.09, t2=0, t3=0, t4=0, t=0.091