1999
DOI: 10.1006/jmaa.1998.6196
|View full text |Cite
|
Sign up to set email alerts
|

A Second-Order Delay Differential Equation with Multiple Periodic Solutions

Abstract: Ž .2 Ž . Žwx. w x The equation xЉ t q x t s bx t y 1 , where и designates the greatest integer function, can be described in brief by two amazing properties. First, for certain values of the coefficients, some or all of its solutions are monotone although the corresponding homogeneous equation is clearly oscillatory. Second, for a specific relation between and b, there exist periodic solutions with different periods. ᮊ

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2

Citation Types

0
8
0

Year Published

2002
2002
2018
2018

Publication Types

Select...
5

Relationship

0
5

Authors

Journals

citations
Cited by 16 publications
(8 citation statements)
references
References 8 publications
0
8
0
Order By: Relevance
“…These equations are first considered by Cooke and Winer [31], Shah and Winer [32]. The existence of periodic solutions and almost periodic solutions were obtained in [33][34][35][36] when delay step κ was confined to 1. Especially, Huang [30] considered the following neural network with piecewise constant argument…”
Section: Introductionmentioning
confidence: 99%
“…These equations are first considered by Cooke and Winer [31], Shah and Winer [32]. The existence of periodic solutions and almost periodic solutions were obtained in [33][34][35][36] when delay step κ was confined to 1. Especially, Huang [30] considered the following neural network with piecewise constant argument…”
Section: Introductionmentioning
confidence: 99%
“…It is well known that KAM theory can be applied to show the existence of quasi periodic motions for periodic ordinary differential equations ( see [11,23] and references therewith). The results about oscillation properties can be found in [1,2,5,16,17,18] and its references therewith. Continuity of a solution at a point joining any two consecutive intervals implies a recursion relation for the values of the solution at such points.…”
Section: Rong Yuan Zampmentioning
confidence: 99%
“…Equation (1.1) has the structure of continuous dynamical system in intervals of unit length. The existence of periodic solutions has been studied in [1,2,5,18] and its references therewith. Therefore, they combine the properties of differential equations and difference equations.…”
Section: Rong Yuan Zampmentioning
confidence: 99%
“…Here g : R ! R is a continuous or at least piecewise continuous function and ½t denotes the greatest integer less than or equal to t. Results on the existence, periodicity and oscillation of solutions of (1.2) can be found in [1,2,6,8]. (1.1) was studied in [3] for construction of g when f is given to be quadratic.…”
Section: Introductionmentioning
confidence: 99%