# krainaksiazek qualitative theory of differential equations 20106996

- znaleziono 13 produktów w 2 sklepach

### 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

### 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 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

### 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

### 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

### Representation and Control of Infinite Dimensional Systems Birkhäuser

**Książki / Literatura obcojęzyczna**

The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from the theoretical and design points of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability and stability. This theory is far more difficult for infinite-dimensional systems such as systems with time delay and distributed parameter systems. In the first place, the difficulty stems from the essential unboundedness of the system operator. Secondly, when control and observation are exercised through the boundary of the domain, the operator representing the sensor and actuator are also often unbounded. §The present book, in two volumes, is in some sense a self-contained account of this theory of quadratic cost optimal control for a large class of infinite-dimensional systems. Volume I deals with the theory of time evolution of controlled infinite-dimensional systems. It contains a reasonably complete account of the necessary semigroup theory and the theory of delay-differential and partial differential equations. Volume II deals with the optimal control of such systems when performance is measured via a quadratic cost. It covers recent work on the boundary control of hyperbolic systems and exact controllability. Some of the material covered here appears for the first time in book form.§The book should be useful for mathematicians and theoretical engineers interested in the field of control.§

Sklep: Libristo.pl

### Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains Elsevier Science Ltd

**Książki / Literatura obcojęzyczna**

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points. The book contains the Hardy Friedrichs Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation. It covers the precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this. It answers the question about the influence of the coefficients smoothness on the regularity of solutions. It has new existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points. It covers: the precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems; the behaviour of weak solutions near conical point for the Dirichlet problem for m Laplacian; the behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration; and, the behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

Sklep: Libristo.pl

### Nonlinear Dynamics and Chaotic Phenomena Springer Netherlands

**Książki / Literatura obcojęzyczna**

FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.

Sklep: Libristo.pl

### Topological Dynamics Betascript Publishing

**Książki / Literatura obcojęzyczna**

High Quality Content by WIKIPEDIA articles! In mathematics, topological dynamics is a branch of the theory of dynamical systems in which qualitative, asymptotic properties of dynamical systems are studied from the viewpoint of general topology.The central object of study in topological dynamics is a topological dynamical system, i.e. a topological space, together with a continuous transformation, a continuous flow, or more generally, a semigroup of continuous transformations of that space. The origins of topological dynamics lie in the study of asymptotical properties of trajectories of systems of autonomous ordinary differential equations, in particular, the behavior of limit sets and various manifestations of "repetitiveness" of the motion, such as periodic trajectories, recurrence and minimality, stability, non-wandering points. George Birkhoff is considered to be the founder of the field. A structure theorem for minimal distal flows proved by Hillel Furstenberg in the early 1960s inspired much work on classification of minimal flows.

Sklep: Libristo.pl

### Structural Mechanics: Modelling and Analysis of Frames and Trusses Wiley-Blackwell (an imprint of John Wiley & Sons...

**Książki / Literatura obcojęzyczna**

Textbook covers the fundamental theory of structural mechanics and the modelling and analysis of frame and truss structures Deals with modelling and analysis of trusses and frames using a systematic matrix formulated displacement method with the language and flexibility of the finite element method Element matrices are established from analytical solutions to the differential equations Provides a strong toolbox with elements and algorithms for computational modelling and numerical exploration of truss and frame structures Discusses the concept of stiffness as a qualitative tool to explain structural behaviour Includes numerous exercises, for some of which the computer software CALFEM is used. In order to support the learning process CALFEM gives the user full overview of the matrices and algorithms used in a finite element analysis

Sklep: Libristo.pl

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