# Oscillations of difference equations with general advanced argument

Open Mathematics (2012)

• Volume: 10, Issue: 2, page 807-823
• ISSN: 2391-5455

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## Abstract

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Consider the first order linear difference equation with general advanced argument and variable coefficients of the form $\nabla x\left(n\right)-p\left(n\right)x\left(\tau \left(n\right)\right)=0,n⩾1,$ where p(n) is a sequence of nonnegative real numbers, τ(n) is a sequence of positive integers such that $\tau \left(n\right)⩾n+1,n⩾1,$ and ▿ denotes the backward difference operator ▿x(n) = x(n) − x(n − 1). Sufficient conditions which guarantee that all solutions oscillate are established. Examples illustrating the results are given.

## How to cite

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George Chatzarakis, and Ioannis Stavroulakis. "Oscillations of difference equations with general advanced argument." Open Mathematics 10.2 (2012): 807-823. <http://eudml.org/doc/269383>.

@article{GeorgeChatzarakis2012,
abstract = {Consider the first order linear difference equation with general advanced argument and variable coefficients of the form $\nabla x(n) - p(n)x(\tau (n)) = 0, n \geqslant 1,$ where p(n) is a sequence of nonnegative real numbers, τ(n) is a sequence of positive integers such that $\tau (n) \geqslant n + 1, n \geqslant 1,$ and ▿ denotes the backward difference operator ▿x(n) = x(n) − x(n − 1). Sufficient conditions which guarantee that all solutions oscillate are established. Examples illustrating the results are given.},
author = {George Chatzarakis, Ioannis Stavroulakis},
journal = {Open Mathematics},
keywords = {General advanced argument; Variable coefficients; Advanced type difference equations; Oscillatory solution; Nonoscillatory solution; general advanced argument; variable coefficients; advanced type difference equations; oscillatory solution; nonoscillatory solution; first order linear difference equation},
language = {eng},
number = {2},
pages = {807-823},
title = {Oscillations of difference equations with general advanced argument},
url = {http://eudml.org/doc/269383},
volume = {10},
year = {2012},
}

TY - JOUR
AU - George Chatzarakis
AU - Ioannis Stavroulakis
TI - Oscillations of difference equations with general advanced argument
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 807
EP - 823
AB - Consider the first order linear difference equation with general advanced argument and variable coefficients of the form $\nabla x(n) - p(n)x(\tau (n)) = 0, n \geqslant 1,$ where p(n) is a sequence of nonnegative real numbers, τ(n) is a sequence of positive integers such that $\tau (n) \geqslant n + 1, n \geqslant 1,$ and ▿ denotes the backward difference operator ▿x(n) = x(n) − x(n − 1). Sufficient conditions which guarantee that all solutions oscillate are established. Examples illustrating the results are given.
LA - eng
KW - General advanced argument; Variable coefficients; Advanced type difference equations; Oscillatory solution; Nonoscillatory solution; general advanced argument; variable coefficients; advanced type difference equations; oscillatory solution; nonoscillatory solution; first order linear difference equation
UR - http://eudml.org/doc/269383
ER -

## References

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1. [1] Berezansky L., Braverman E., Pinelas S., On nonoscillation of mixed advanced-delay differential equations with positive and negative coefficients, Comput. Math. Appl., 2009, 58(4), 766–775 http://dx.doi.org/10.1016/j.camwa.2009.04.010 Zbl1197.34118
2. [2] Chatzarakis G.E., Koplatadze R., Stavroulakis I.P., Optimal oscillation criteria for first order difference equations with delay argument, Pacific J. Math., 2008, 235(1), 15–33 http://dx.doi.org/10.2140/pjm.2008.235.15 Zbl1153.39010
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12. [12] Li X., Zhu D., Oscillation and nonoscillation of advanced differential equations with variable coefficients, J. Math. Anal. Appl., 2002, 269(2), 462–488 http://dx.doi.org/10.1016/S0022-247X(02)00029-X Zbl1013.34067
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