2 edition of On the stability of differential equations with periodic coefficients found in the catalog.
On the stability of differential equations with periodic coefficients
|Statement||by Jan Boman.|
|Series||Transactions of the Royal Institute of Technology, Stockholm, Sweden ; nr. 180, Pure and applied mathematics and physics ; 18|
|LC Classifications||MLCM 84/1342 (Q)|
|The Physical Object|
|Pagination||20 p. : ill. ; 25 cm.|
|Number of Pages||25|
|LC Control Number||84128945|
The stability of periodic solutions of these systems are analyzed by using the semidiscretization method. By employing this method, the periodic coefficients and the delay terms are approximated as constants over a time interval, and the delay differential system is reduced to a set of linear differential equations in this time by: Book Description. Singular Differential Equations and Special Functions is the fifth book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume a set they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology.. This fifth book consists of one chapter (chapter 9 of the set).
In this paper, we develop Galerkin approximations for determining the stability of delay differential equations (DDEs) with time periodic coefficients and time periodic delays. Using a transformation, we convert the DDE into a partial differential Cited by: 8. This book's discussion of a broad class of differential equations will appeal to professionals as well as graduate students. Beginning with the structure of the solution space and the stability and periodic properties of linear ordinary and Volterra differential equations, the text proceeds to an extensive collection of applied problems.4/5(1).
those derived in Chapter 5 for linear differential equations with constant or periodic coefficients as special cases. Stability properties of general linear differential equations with linear or nonlinear perturbations are also studied using the variation of parameters formula and Gronwall’ s inequality. In. In [15–20] we studied the question about the asymptotic stability of solutions to systems of ordinary differential equations and systems of delay differential equations with periodic proved theorems on asymptotic stability which are analogs of the classic theorems on the asymptotic stability for equations with constant : Gennadii V Demidenko, Inessa I Matveeva.
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Full text Full text is available as a scanned copy of the original print version. Get a printable copy (PDF file) of the complete article (K), or click on a page image below to browse page by by: 5.
A chapter is then devoted to the linear equation with constant coefficients. The two following chapters are introductory discussions of stability theory for autonomous and nonautonomous systems. Included here are two results for nonlinear systems, Liapunov’s direct method, and some results for the second-order linear by: PDF | On May 1,F.
Dannan and others published On the stability of the solutions of second order differential equations with periodic coefficients | Find, read and cite all the research. On the stability of the solutions of second order differential equations with periodic coefficients F.
Dannan 1 Ukrainian Mathematical Journal vol Author: F. Dannan. Publisher Summary. This chapter discusses problems leading to periodic differential equations. In some practical problems, the differential equations with periodic coefficients occur naturally because some factor in the problem is itself periodic; these are mainly problems in connection with oscillations or in electronic circuits, but a notable case is that of Hill's equation that occurred in.
ON THE STABILITY OF THE SOLUTIONS OF A SYSTEM OF HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS WITH PERIODIC (AND OTHER) COEFFICIENTS (OB USTOICHIVOSTI RESHENII SISTEtlY LINEINYKH ODNORODNYKH DIFFERENTSIAL'NYKH URAVNENII S PERIODICHESKIMI (I DRUGIMI) KOEFPITSIYENTAMI) PMM Vol, No.5, pp.
N.P. Author: N.P. Erugin. Under study are the systems of quasilinear delay differential equations with periodic coefficients of linear terms. Mathematical Formulation of the Stability Concept and Basic Results Stability in Conservative Systems and the KAM Theorem Averaging and the Stability of Perturbed Periodic Orbits.
diﬀerential equation with real periodic coeﬃcients, also known by the name Hill’s equation, with emphasis on stability and instability intervals and the diﬀerential operatortheoryconnected with thisproblematic.
These equations are used as a model in solid state physics. It is our aim to get this topic. Stability theory of differential equations Richard Bellman Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations.
This book's discussion of a broad class of differential equations will appeal to professionals as well as graduate students. Beginning with the structure of the solution space and the stability and periodic properties of linear ordinary and Volterra differential equations, the text proceeds to an extensive collection of applied by: Linear system of differential equations with periodic coefficients.
A system of linear ordinary differential equations of the form. where is a real variable, and are complex-valued functions, and. The number is called the period of the coefficients of the system (1).
This book explains the following topics: First Order Equations, Numerical Methods, Applications of First Order Equations1em, Linear Second Order Equations, Applcations of Linear Second Order Equations, Series Solutions of Linear Second Order Equations, Laplace Transforms, Linear Higher Order Equations, Linear Systems of Differential Equations, Boundary Value Problems and Fourier.
This book discusses as well nonlinear hyperbolic equations in further contributions, featuring stability properties of periodic and almost periodic solutions.
The reader is also introduced to the stability problem of the equilibrium of a chemical network. The final chapter deals with suitable spaces for studying functional Edition: 1. This concise text offers undergraduates in mathematics and science a thorough and systematic first course in elementary differential equations.
Presuming a knowledge of basic calculus, the book first reviews the mathematical essentials required to 3/5(1). The behaviour of solutions to certain second order nonlinear delay differential equations with variable deviating arguments is discussed.
The main procedure lies in the properties of a complete Lyapunov functional which is used to obtain suitable criteria to guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately by: 2.
Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the Reviews: 1.
This is a brief, modern introduction to the subject of ordinary differential equations, with an emphasis on stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for the advanced undergraduate or beginning graduate student who has had a first course in ordinary differential equations/5(2).
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments.
It is intended as a text for a first graduate course in differential equations for students in Book Edition: 1. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.
Stability of the ODE with periodic coefficients / Periodic solutions. Ask Question Browse other questions tagged ordinary-differential-equations or ask your own question.
I have a non linear first order ordinary differential equation with periodic coefficients. I am trying to prove that the periodic solution of the differential equation exists.
I am giving you an example of the problem I am having.Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to periodic linear differential equations of the form ˙ = (), with () a piecewise continuous periodic function with period and defines the state of the stability of solutions.
The main theorem of Floquet theory, Floquet's theorem, due to Gaston Floquet (), gives a canonical form for.In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions.
The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle.