Last edited by Gazragore
Monday, April 20, 2020 | History

3 edition of Some results concerning periodic solutions to periodic differential equations found in the catalog.

Some results concerning periodic solutions to periodic differential equations

Kurt Munk Andersen

Some results concerning periodic solutions to periodic differential equations

  • 162 Want to read
  • 38 Currently reading

Published by Mathematical Institute, Technical University of Denmark in Lyngby .
Written in English

    Subjects:
  • Differential equations -- Numerical solutions.,
  • Periodic functions.

  • Edition Notes

    StatementKurt Munk Andersen and Allan Sandqvist.
    SeriesMAT report ; no. 50
    ContributionsSandqvist, Allan, joint author.
    Classifications
    LC ClassificationsQA371 .A578
    The Physical Object
    Pagination8 leaves ;
    ID Numbers
    Open LibraryOL4198610M
    LC Control Number80477551

    Luigi Amerio (15 August – 28 September ), was an Italian electrical engineer and is known for his work on almost periodic functions, on Laplace transforms in one and several dimensions, and on the theory of elliptic partial differential equationsAlma mater: Polytechnic University of Milan.   In this section we will work quick examples illustrating the use of undetermined coefficients and variation of parameters to solve nonhomogeneous systems of differential equations. The method of undetermined coefficients will work pretty much as it does for nth order differential equations, while variation of parameters will need some extra derivation work to get . Additionally, we show how our results are complementary to a result of Arnold [] concerning the infinite time behavior of adiabatic invariants in Hamiltonian systems. We illustrate this by using our method to prove the existence of Smale horseshoes for a pendulum whose length undergoes a slow periodic by: 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.

    the type (). There, we derive some results about the existence of infinitely many periodic solutions of () which extend Theorem 1. This paper is thus organized as follows: 1. introduction and main results. 2. A theorem on the homotopy groups of level sets of a functional. 3. Critical values and periodic solutions in the autonomous case.


Share this book
You might also like
Providing for the consideration of H.R. 1252, the Judicial Reform Act of 1998

Providing for the consideration of H.R. 1252, the Judicial Reform Act of 1998

Patterns of human motion

Patterns of human motion

A household survey of economic goods on Romonum Island, Truk

A household survey of economic goods on Romonum Island, Truk

The golden age of opera (Opera biographies)

The golden age of opera (Opera biographies)

Report of the Select Committee on Disabilities of British Indians in Transvaal

Report of the Select Committee on Disabilities of British Indians in Transvaal

Germ

Germ

prophesies of Nostradamus

prophesies of Nostradamus

Japanese banks in the US

Japanese banks in the US

Towards an entrepreneurial culture for the twenty-first century

Towards an entrepreneurial culture for the twenty-first century

The dramatic works of J.C. Cross, stage manager of the Surrey Theatre

The dramatic works of J.C. Cross, stage manager of the Surrey Theatre

Land and democracy in Zimbabwe

Land and democracy in Zimbabwe

Some results concerning periodic solutions to periodic differential equations by Kurt Munk Andersen Download PDF EPUB FB2

Differential Equations is a collection of papers from the "Eight Fall Conference on Differential Equations" held at Oklahoma State University in October The papers discuss hyperbolic problems, bifurcation function, boundary value problems for Lipschitz equations, and the periodic solutions of systems of ordinary differential equations.

Since then, the existence of pseudo-almost periodic solutions to differential equations, partial differential equations and functional differential equations has been of a great interest to Author: Toka Diagana. Existence results concerning almost periodic and asymptotically almost periodic solutions to ordinary neutral differential equations and abstract partial neutral differential equations have.

where the coefficient functions a(x)ß(x) and y(x) are continuous, positive and periodic. We obtain, in some sense, generalizations of results contained in [] and [], where ß(x) is assumed identically homoclinic solution u of equation (I) Cited by: 1. This chapter focuses on the bifurcation theory and periodic solutions of some autonomous functional differential equations.

A number of authors have Some results concerning periodic solutions to periodic differential equations book nonlinear, autonomous functional differential bifurcation theorem that implies the known existence results for periodic solutions and also new information concerning the structure of the set of periodic solutions, Author: Roger D.

Nussbaum. general nonlinear differential equations. Chapter Periodic Solutions. In Section 1, we give some basic results concerning Some results concerning periodic solutions to periodic differential equations book search of periodic solutions and indicate that it is appropriate to use a fixed point approach.

In Section 2, we derive the existence of periodic solutions for general linear differential equations. First, we derive. This book provides an introduction to ordinary differential equations and dynamical systems.

We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial conditions. In this work we present some new results concerning the existence of solutions for first-order nonlinear integro-differential equations with boundary value conditions.

Our methods to prove the existence of solutions involve new differential inequalities and classical fixed-point theorems. MR()Subject Classification. 34D09,34DCited by: 3. This book's discussion of a broad class of differential equations will appeal to professionals as well Some results concerning periodic solutions to periodic differential equations book 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 :   Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener [], and Shah and Wiener [], usually describe hybrid dynamical systems (a combination of continuous and discrete) and so combine properties of both differential and difference the years, great attention has been paid to the study of the Author: Li Wang, Chuanyi Some results concerning periodic solutions to periodic differential equations book.

This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. and electrical engineering are investigated.

Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Then the fundamental results concerning the. " : The Tragedy of Man J.C.W. Horne's translation In this book I tried to sum up the facts and results I considered most important concerning periodic solutions of ordinary differential equations (ODEs) produced by this century from Henri Poincare up to the youngest mathematician appearing in the list of references.

1. Introduction and Preliminaries Almost periodic and asymptotically almost periodic solutions of differential equations in Banach spaces have been considered by many authors so far (for the basic information on the subject, we.

" : The Tragedy of Man J.C.W. Horne's translation In this book I tried to sum up the facts and results I considered most important concerning periodic solutions of ordinary differential equations (ODEs) produced by this century from Henri Poincare up to the youngest mathematician appearing in the list of : Springer-Verlag New York.

Excerpts from the Abstract: This book provides an introduction to ordinary differential equations and dynamical start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial conditions.

results which guarantees the existence of periodic solutions of the equation having the same period as the periodic input. Thcsc results prevail also when the unforced equation has “chaotic” solutions.

Thus, our results indicate that “chaos” may be removed through external forcing. ( views) Ordinary Differential Equations and Dynamical Systems by Gerald Teschl - Universitaet Wien, This book provides an introduction to ordinary differential equations and dynamical systems.

We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem. Get this from a library. Periodic Motions. [Miklós Farkas] -- This book sums up the most important results concerning the existence and stability of periodic solutions of ordinary differential equations achieved in the twentieth century along with relevant.

Please submit book proposals to Jürgen Appell. Titles in planning include. Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations () Tomasz W.

Dłotko and Yejuan Wang, Critical Parabolic-Type Problems () Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective ().

The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness. The second part describes the basic results concerning linear differential equations, while the third deals with nonlinear equations.

In the last part the authors write about the basic results concerning power series solutions. The object of this paper is to prove existence theorems concerning bounded, periodic, and almost periodic solutions of system (1) and investigate some of their asymptotic properties.

Since the special case p(t, x, 2) = p(k) and /3(x) = B. x, where B is a positive. In Section 3 we derive a new form of the radiation term. In Section 4 we formulate a periodic problem and give some preliminary assertions. In Section 5 we give an operator formulation of the periodic problem and by a suitable fixed point theorem prove an existence-uniqueness of periodic solution for Dirac : Vasil Angelov.

Abstract. This book provides an introduction to ordinary di erential equations and dynamical systems. We start with some simple examples of explicitly solvable equations.

Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial Size: 3MB. In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative.

A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to Author: Dandan Yang, Chuanzhi Bai.

Almost-periodic solutions of differential equations with diagonal operators --VIII. Weakly almost-periodic solutions of some abstract differential equations --IX.

Mild solutions with generalized normality property --X. Uniqueness of bounded ultraweak solutions to the equation u'(t) = a(t)Au(t) in Hilbert spaces --XI.

Contents Preface to the fourth edition vii 1 Second-order differential equations in the phase plane 1 Phase diagram for the pendulum equation 1 Autonomous equations in the phase plane 5 Mechanical analogy for the conservative system x¨=f(x) 14 The damped linear oscillator 21 Nonlinear damping: limit cycles 25 Some applications 32 Parameter-dependent File Size: 6MB.

Office of University Affairs, NASA Aug Page 2 qr periodic solutions of perturbed nonlinear systems x = f(t,x) + g(t,x). Many of the theorems concerning the perturbed linear system may be proved for the perturbed nonlinear system.

One obvious benefit of such theorems is that previously the internal nonlinearities of such systems were. Abstract. This book provides an introduction to ordinary di erential equa-tions and dynamical systems. We start with some simple examples of explic-itly solvable equations.

Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial conditions. of almost periodic solutions of functional-differential equations. In this chapter; therefore, we give a "brief discussion of the development of almost periodicity and functional-differential equations.

Almost periodicity as a structural property of functions is a generalization of "pure" periodicity. Free oscillations of undamped. You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read.

Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

Book Description. Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of nonlinear equations.

of periodic, slowly oscillating, solutions of autonomous delay differential equations. Following the early work of Jones [l], Wright [2] and Grafton [3], the work of Nussbaum [4, 51 is to be specially noted for providing several new fixed point results and a global bifurcation theorem.

In general, to obtain analytically periodic solutions of a differential system, is a very difficult problem, many times impossible.

Here using the averaging theory this difficult problem for the differential equations (2) is reduced to find the zeros of. 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.

Abstract. This book provides a self-contained introduction to ordinary di erential equations and dynamical systems suitable for beginning graduate students. In the rst part we begin with some simple examples of explicitly solvable equations and a rst glance at qualitative methods.

Then we prove the fundamental results concerning the initial. Equations with periodic coefficients Conjugacies between linear equations Exercises of ordinary differential equations.

The book can be used as a basis for a second course of ordinary differen­ tion of some results in Chapters 8 and 9 concerning more advanced topics. () Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem.

Journal of Differential Equations() Nonlinear scalar model of a suspension bridge: existence of multiple periodic by:   The forced sine-Gordon equation can be considered as a natural extension to partial differential equations of the forced pendulum equation.

It is known that, if f is almost periodic and not too large, the pendulum equation has almost periodic solutions. Our aim is to extend this result to the sine-Gordon equation. Overall, this book is a solid graduate-level introduction to ordinary differential equations, especially for applications.

It is reminiscent of the classic texts of Birkhoff and Rota and of Coddington and Levinson, rather than, say, the recently updated book.

Ten Mathematical Essays on Approximation in Analysis and Topology the intra-history of the the genesis of the first general global continuation results in the context of periodic solutions of nonlinear periodic systems, as well as the genesis of the coincidence degree, some novel applications of the topological degree for ascertaining the.

Purchase Non-Linear Differential Equations, Volume 67 - 1st Edition. Print Book & E-Book. ISBNBook Edition: 1. This paper provides some results download pdf the existence of periodic solutions for Hamiltonian systems which may be considered as time-periodic perturbations of an autonomous system of the type.

𝒥 ⁢ z ˙ = ∇ ⁡ ℋ ⁢ (z). (HS) Here, ℋ: ℝ 2 ⁢ N → ℝ is a continuously differentiable function and 𝒥 is the standard symplectic matrix Cited by:   Designed for ebook rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of nonlinear equations.