On the second-order differential equation with piecewise constant argument and almost periodic coefficients
type: Item
instance of: scholarly article
title: On the second-order differential equation with piecewise constant argument and almost periodic coefficients
zbMATH Open document ID: 1029.34058
DOI: 10.1016/S0362-546X(02)00172-4
author: Rong Yuan
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-03-11T00:00:00Z
review text: Here, the author studies the existence of almost- and quasi-periodic solutions to two classes of second-order differential equations. As a corollary, it is shown that periodic and unbounded solutions can coexist for the equation \(x''(t)+\omega^2x(t)=bx([t])+f(t)\), which is different from the case: \(b=0\). This phenomenon is due to the piecewise constant argument and illustrates a crucial difference between ordinary differential equations with piecewise constant argument. The results are extended to nonlinear equations.
Mathematics Subject Classification ID: 34K14
zbMATH DE Number: 1880103
zbMATH Keywords: almost-periodic solutions
zbMATH Keywords: quasi-periodic solutions
zbMATH Keywords: delay equations
zbMATH Keywords: piecewise constant argument
Wikidata QID: Q115339197
MaRDI profile type: Publication
cites work: Oscillatory and Periodic Solutions of Delay Differential Equations with Piecewise Constant Argument
cites work: Q3657815
cites work: Retarded differential equations with piecewise constant delays
cites work: Q3975198
cites work: Q5563566
cites work: Almost periodic differential equations
cites work: On quasi-periodic solutions of differential equations with piecewise constant argument
cites work: On Almost Periodic Solutions of a Class of Differential Equations
cites work: Advanced differential equations with piecewise constant argument deviations
cites work: Q4858399
cites work: A second-order delay differential equation with multiple periodic solutions
cites work: Excitability of a second-order delay differential equation
cites work: Complicated dynamics in a delay Klein–Gordon equation
cites work: Existence of almost-periodic solutions to second-order neutral delay differential equations with piecewise constant argument
cites work: Almost periodic solutions of a class of singularly perturbed differential equations with piecewise constant argument
cites work: On the existence of almost periodic solutions of a singularly perturbed differential equation with piecewise constant argument
cites work: On the regular solution of a second order delay differential equation
cites work: ALMOST PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT
cites work: The existence of almost periodic solutions for a class of differential equations with piecewise constant argument
full work available at URL: s0362-546x(02)00172-4
OpenAlex ID: W2092701755
Recommended article: On the spectrum of almost periodic solution of second-order differential equations with piecewise constant argument
Recommended article: On almost periodic solution of differential equations with piecewise constant argument
Recommended article: Almost periodic solutions of second-order neutral equations with piecewise constant arguments
Recommended article: Q3072809
Recommended article: Q4649324
Recommended article: ALMOST PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT
Recommended article: Q4549043
Recommended article: Q3154209
Recommended article: Existence and uniqueness of periodic solutions for a second-order nonlinear differential equation with piecewise constant argument
Recommended article: Q5400224
description: scientific article; zbMATH DE number 1880103