Oscillation criteria for \(n\)th-order forced functional-differential equations
type: Item
instance of: scholarly article
title: Oscillation criteria for \(n\)th-order forced functional-differential equations
zbMATH Open document ID: 1032.34065
DOI: 10.1016/S0022-247X(03)00022-2
author: Devrim Çakmak
author: Aydin Tiryaki
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-25T00:00:00Z
review text: Using the method of general means, the authors present some new oscillation criteria for forced functional-differential equations of the form \[ x^{(n)}(t)+\sum_{i=1}^{n-1}a_ix^{(i)}(t)+q(t)f(x(g(t)))=e(t), \] where \(a_i\) are real constants, \(q(t),\;f(x),\;e(t)\), and \(g(t)\) are real continuous functions, \(xf(x)>0\) for \(x\neq 0\), and \(\lim_{t\to\infty}g(t)=\infty\). The same technique is used to establish some oscillation criteria for the forced neutral differential equation of the form \[ (x(t)+\delta(t)x(t-\tau))^{(n)}+ \sum_{i=1}^{n-1}a_i(x(t)+\delta(t)x(t-\tau))^{(i)}+ f(t,x(g(t)),x'(\sigma(t)))=e(t), \] and the neutral equation of the form \[ \begin{multlined} (x(t)+\delta x(t-\tau))^{(n)}+ \sum_{i=1}^{n-1}a_i(x(t)+\delta x(t-\tau))^{(i)}+q(t)x(t)+ b(t)x(t-\tau)\\ =e(t)+c(t)f_1(x(t))+d(t)f_2(x(t-\tau)), \end{multlined} \] where \(xf_1(x)>0\) and \(xf_2(x)>0\) for \(x\neq 0, n\geq 1\), \(\tau, \delta\) are nonnegative constants, \(q(t)>0\), \(b(t)>0\), \(c(t)>0\), and \(d(t)>0\).
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 1915728
zbMATH Keywords: oscillation theory
zbMATH Keywords: \(n\)th-order forced functional-differential equations
reviewed by: Jan Ohriska
MaRDI profile type: Publication
cites work: Forced oscillation of \(n\)th-order nonlinear differential equations
cites work: Asymptotic and oscillatory behavior of \(n\)th order forced functional differential equations
cites work: Oscillatory behavior of \(n\)th order forced functional differential equations
cites work: On the maintenance of oscillations of \(n\)-th order equations under the effect of a small forcing term
cites work: Maintenance of Oscillations Under the Effect of a Periodic Forcing Term
cites work: Q4134269
cites work: The oscillation of a forced equation implies the oscillation of the unforced equation - small forcings
cites work: Oscillation of functional differential equations with general deviating arguments
cites work: Forced oscillation of \(n\)th-order functional differential equations
cites work: Second Order Nonlinear Forced Oscillations
cites work: Oscillation criteria for a forced second-order linear differential equation
cites work: Oscillation criteria for second order nonlinear differential equations involving general means
description: scientific article; zbMATH DE number 1915728