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Discrete Dynamics in Nature and Society
Article . 2011 . Peer-reviewed
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Discrete Dynamics in Nature and Society
Article
License: CC BY
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Article . 2011
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Oscillation of Certain Second‐Order Sub‐Half‐Linear Neutral Impulsive Differential Equations

Oscillation of certain second-order sub-half-linear neutral impulsive differential equations
Authors: Sun, Yuangong(School of Mathematics, University of Jinan);

Oscillation of Certain Second‐Order Sub‐Half‐Linear Neutral Impulsive Differential Equations

Abstract

By introducing auxiliary functions, we investigate the oscillation of a class of second‐order sub‐half‐linear neutral impulsive differential equations of the form [r(t)ϕβ(z′(t))] ′ + p(t)ϕα(x(σ(t))) = 0, t ≠ θk, where β > α > 0, z(t) = x(t) + λ(t)x(τ(t)). Several oscillation criteria for the above equation are established in both the case 0 ≤ λ(t) ≤ 1 and the case −1 < −μ ≤ λ(t) ≤ 0, which generalize and complement some existing results in the literature. Two examples are also given to illustrate the effect of impulses on the oscillatory behavior of solutions to the equation.

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Keywords

Oscillation theory of functional-differential equations, QA1-939, Functional-differential equations with impulses, Mathematics

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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!
0
Average
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