Oscillatory properties of second order half-linear difference equations

Pavel Řehák

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 2, page 303-321
  • ISSN: 0011-4642

Abstract

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We study oscillatory properties of the second order half-linear difference equation Δ ( r k | Δ y k | α - 2 Δ y k ) - p k | y k + 1 | α - 2 y k + 1 = 0 , α > 1 . ( HL ) It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation Δ ( r k Δ y k ) - p k y k + 1 = 0 . We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.

How to cite

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Řehák, Pavel. "Oscillatory properties of second order half-linear difference equations." Czechoslovak Mathematical Journal 51.2 (2001): 303-321. <http://eudml.org/doc/30636>.

@article{Řehák2001,
abstract = {We study oscillatory properties of the second order half-linear difference equation \[ \Delta (r\_k|\Delta y\_k|^\{\alpha -2\}\Delta y\_k)-p\_k|y\_\{k+1\}|^\{\alpha -2\}y\_\{k+1\}=0, \quad \alpha >1. \qquad \mathrm \{(HL)\}\] It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation \[ \Delta (r\_k\Delta y\_k)-p\_ky\_\{k+1\}=0. \] We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.},
author = {Řehák, Pavel},
journal = {Czechoslovak Mathematical Journal},
keywords = {half-linear difference equation; Picone identity; Reid Roundabout Theorem; oscillation criteria; half-linear difference equation; Picone identity; Reid Roundabout theorem; oscillation criteria},
language = {eng},
number = {2},
pages = {303-321},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillatory properties of second order half-linear difference equations},
url = {http://eudml.org/doc/30636},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Řehák, Pavel
TI - Oscillatory properties of second order half-linear difference equations
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 2
SP - 303
EP - 321
AB - We study oscillatory properties of the second order half-linear difference equation \[ \Delta (r_k|\Delta y_k|^{\alpha -2}\Delta y_k)-p_k|y_{k+1}|^{\alpha -2}y_{k+1}=0, \quad \alpha >1. \qquad \mathrm {(HL)}\] It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation \[ \Delta (r_k\Delta y_k)-p_ky_{k+1}=0. \] We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.
LA - eng
KW - half-linear difference equation; Picone identity; Reid Roundabout Theorem; oscillation criteria; half-linear difference equation; Picone identity; Reid Roundabout theorem; oscillation criteria
UR - http://eudml.org/doc/30636
ER -

References

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