# Oscillations of difference equations with general advanced argument

George Chatzarakis; Ioannis Stavroulakis

Open Mathematics (2012)

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

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topGeorge 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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