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

- 162 Want to read
- 38 Currently reading

Published
**1979** by Mathematical Institute, Technical University of Denmark in Lyngby .

Written in English

- Differential equations -- Numerical solutions.,
- Periodic functions.

**Edition Notes**

Statement | Kurt Munk Andersen and Allan Sandqvist. |

Series | MAT report ; no. 50 |

Contributions | Sandqvist, Allan, joint author. |

Classifications | |
---|---|

LC Classifications | QA371 .A578 |

The Physical Object | |

Pagination | 8 leaves ; |

ID Numbers | |

Open Library | OL4198610M |

LC Control Number | 80477551 |

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.

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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.

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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.

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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.

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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.

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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.

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

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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.

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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.