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Saturday, August 8, 2020 | History

2 edition of Periodic solutions of neutral differential equations found in the catalog.

Periodic solutions of neutral differential equations

Zhang YI

Periodic solutions of neutral differential equations

by Zhang YI

  • 14 Want to read
  • 15 Currently reading

Published by University ofSheffield, Dept. of Control Engineering in Sheffield .
Written in English


Edition Notes

Statementby Zhang YI, S.P. Banks and Y. Zhang.
SeriesResearch report / University of Sheffield. Department of Control Engineering -- no.390, Research report (Universityof Sheffield. Department of Control Engineering) -- no.390.
ContributionsBanks, Stephen P. 1949-, Zhang, Y.
ID Numbers
Open LibraryOL13964069M

Get this book in print. Appendix Arscott basically-periodic solutions behaviour Bessel function ce2n cen Periodic differential equations: an introduction to Mathieu, Lamé, and allied functions Volume 66 of International series of monographs in pure and applied mathematics. Chapter 4 develops the recent theory of dissipative systems. Chapter 9 is a new chapter on perturbed systems. Chapter 11 is a new presentation incorporating recent results on the existence of periodic solutions of autonomous equations. Chapter 12 Brand: Springer-Verlag New York.

It is known that if a periodic neutral differential equation of certain type (which includes equations like $({d / dt})[ {x(t) - q \times ({t - r})} ] = f({x Cited by: The authors have tried to provide a complete bibliography of all relevant publications (their number reaches about ) from the theory of time-periodic solutions to non-linear partial and abstract differential equations whose origin may be put in the early thirties of this by:

Chegg's differential equations experts can provide answers and solutions to virtually any differential equations problem, often in as little as 2 hours. Thousands of differential equations guided textbook solutions, and expert differential equations answers when you need them. Samoilenko and Ronto [] assume the numerical-analytic method to study the periodic solutions for ordinary differential equations and its algorithm structure and this method includes uniform sequences of periodic functions and the results of that study are using the periodic solutions on wide range in the difference of new processes industry and by: 7.


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Periodic solutions of neutral differential equations by Zhang YI Download PDF EPUB FB2

Periodic Differential Equations: An Introduction to Mathieu, Lamé, and Allied Functions covers the fundamental problems and techniques of solution of periodic differential equations.

This book is composed of 10 chapters that present important equations and the special functions they generate, ranging from Mathieu's equation to the intractable ellipsoidal Book Edition: 1. Keywords-Neutral difference equations, Delay difference equations, Convex equations, Finite delay, Infinite delay, Periodic solutions, Bounded solutions, Massera theorem.

INTRODUCTION It is well known that for linear periodic ordinary differential equations, the existence of a bounded solution implies the existence of a periodic solution as Cited by: 4. where f ∈ C (ℝ, ℝ),and N ≥ 2 is an integer. Kaplan and Yorke [] introduced a technique of couple system which allows them to reduce the search for periodic solutions of a differential delay equation to the problem of finding periodic solutions for a related system of ordinary differential study periodic solutions of () with N = 2, f ∈ C (ℝ, ℝ) is Cited by: 9.

where Periodic solutions of neutral differential equations book, are closed linear operators; is a Banach space; the history, belongs to some abstract phase space defined axiomatically are appropriated functions.

The study of abstract neutral equations is motivated by different practical applications in different technical fields. The literature related to ordinary neutral functional differential equations is Cited by: In this paper we study a non-autonomous neutral functional differential equation in a Banach space.

Applying the theory of semigroups of operators to evolution equations and Krasnoselskii’s fixed point theorem we establish the existence and uniqueness of a mild almost periodic solution of the problem under by:   We investigate the existence of almost-periodic weak solutions of second-order neutral delay-differential equations with piecewise constant argument of the form, where denotes the greatest integer function, is a real nonzero constant, and is almost : Li Wang, Chuanyi Zhang.

Periodic Solution Functional Differential Equation Topological Degree Neutral Type Index Zero These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm by: 1.

A survey on periodic solutions of differential equations is. For autonomous systems there is translation invariance: if is a periodic solution, then is also a periodic solution.

This is related to the presence of one multiplier with value 1. For periodic solutions with period one may replace the time variable by a phase variable. The phase. The study on neutral functional differential equations is more intricate than ordinary delay differential equations, that is why comparing plenty of results on.

where is a constant matrix and is an absolutely-continuous matrix function, periodic with period, non-singular for all, and such sely, if and are matrices with the given properties, then the matrix (5) is the transition matrix of an equation (3) with -periodic matrix, called the indicator matrix, and the matrix function in the representation (5) are not uniquely.

How to prove existence of periodic solutions of ordinary differential equations. Ask Question Asked 7 years, So, the best we can hope for is the existence of some periodic solution. The book by Deimling which I mentioned gives a number of methods to obtain such an existence result. Series Solutions to Differential Equations.

It had been proved that for linear neutral functional differential equations of D-operator type with infinite delay, there was a periodic solution if and only if there was a bounded solution.

View. We consider a kind of second-order neutral functional differential equation. On the basis of Mawhin&#x;s coincidence degree, the existence and uniqueness of periodic solutions are proved. It is indicated that the result is related to the deviating arguments. Moreover, we present two simulations to demonstrate the validity of analytical : Na Wang.

Periodic Solutions Periodic solutions of equations are solutions that describe regularly repeating processes. In such branches of science as the theory of oscillations and celestial mechanics, periodic solutions of systems of differential equations are of special interest.

A periodic solution yi = Φi (t) of (1) consists of periodic functions of t that. Periodic Differential Equations: An Introduction to Mathieu, Lamé, and Allied Functions covers the fundamental problems and techniques of solution of periodic differential equations. This book is composed of 10 chapters that present important equations and the special functions they generate, ranging from Mathieu's equation to the intractable ellipsoidal.

uniqueness of weighted pseudo periodic solution of class r that are solutions to neutral functional di erential equations. Other applications to partial dif-ferential equations and scalar reaction-di usion equations with delay are also given.

Introduction The existence periodic solutions is one of the most interesting and important topics in. PERIODIC NEUTRAL DIFFERENTIAL EQUATIONS 73 n x n matrix function of bounded variation on 8, y is continuous and ~(0, t) = 0 for any t 2 0.

If f:R, x C+E” is a continuous function, then the relation (44 w, Xt) = fk Xt) is a NFDE. A solution through p at time o is a. a linear differential equation with periodic coefficients. Ask Question Asked 4 years, Thanks for contributing an answer to Mathematics Stack Exchange.

How to prove existence of periodic solutions of ordinary differential equations. Periodic differential equation proof.

Abstract. In this paper, we discuss the properties of the neutral operator, and by applying coincidence degree theory and fixed point index theory, we obtain sufficient conditions for the existence, multiplicity, and nonexistence of (positive) periodic solutions to two kinds of second-order differential equations with the prescribed neutral by: 9.

CONTENTS Application Modules vii Preface ix About the Cover viii CHAPTER 1 First-Order Differential Equations 1 Differential Equations and Mathematical Models 1 Integrals as General and Particular Solutions 10 Slope Fields and Solution Curves 19 Separable Equations and Applications 32 Linear First-Order Equations 48 Substitution Methods.

On the existence of quasi periodic and almost periodic solutions of neutral functional differential equations.

Communications on Pure & Applied Analysis,3 (2): doi: /cpaaCited by: In class we discussed some aspects of periodic solutions of ordinary differential equations. From the questions I received, my presentation was not so clear.

Here I’ll give a detailed formal proof for the first order equation u0(x)+a(x)u(x)= f(x) (1) where both a(x) and f(x) are periodic with period P, so, for instance, a(x+P)=a(x) for all x.We study the asymptotic behaviour of the solutions of a class of linear neutral delay differential equations with discrete delay where the coefficients of the non neutral part are periodic functions which are rational multiples of all time delays.

We show that this technique is applicable to a broader class where the coefficients of the neutral part are periodic functions as by: 1.