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

Abstract

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Consider the first order linear difference equation with general advanced argument and variable coefficients of the form ∇ x ( n ) - p ( n ) x ( τ ( n ) ) = 0 , n ⩾ 1 , where p(n) is a sequence of nonnegative real numbers, τ(n) is a sequence of positive integers such that τ ( n ) ⩾ 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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  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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