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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Annali di Matematica...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Annali di Matematica Pura ed Applicata (1923 -)
Article . 1987 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1987
Data sources: zbMATH Open
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Oscillation and asymptotic behavior of second order neutral differential equations

Authors: Grammatikopoulos, M. K.; Ladas, G.; Meimaridou, A.;

Oscillation and asymptotic behavior of second order neutral differential equations

Abstract

The authors consider the following second order differential equation \[ (1)\quad \frac{d^ 2}{dt^ 2}[y(t)+P(t)y(t-\tau)]+Q(t)y(t- \sigma)=0,\quad t\geq t_ 0,\quad \tau,\sigma \geq 0 \] with \(P,Q\in C([t_ 0,\infty],{\mathbb{R}})\), where the highest derivate of the unknown function appears both with delays \(\tau\) and \(\sigma\) in some terms and without delays in some others. Such equation is called neutral delay differential equation. In this paper the authors investigate the asymptotic behavior of the nonoscillatory solutions of (1) and find sufficient conditions for the oscillation of all solutions; of all bounded solutions; all unbounded solutions.

Keywords

second order differential equation, nonoscillatory solutions, Functional-differential equations (including equations with delayed, advanced or state-dependent argument), Asymptotic expansions of solutions to ordinary differential equations, Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations, neutral delay differential equation

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
15
Average
Top 10%
Average
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