On oscillation and nonoscillation properties of Emden-Fowler difference equations

Mariella Cecchi; Zuzana Došlá; Mauro Marini

Open Mathematics (2009)

  • Volume: 7, Issue: 2, page 322-334
  • ISSN: 2391-5455

Abstract

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A characterization of oscillation and nonoscillation of the Emden-Fowler difference equation is given, jointly with some asymptotic properties. The problem of the coexistence of all possible types of nonoscillatory solutions is also considered and a comparison with recent analogous results, stated in the half-linear case, is made.

How to cite

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Mariella Cecchi, Zuzana Došlá, and Mauro Marini. "On oscillation and nonoscillation properties of Emden-Fowler difference equations." Open Mathematics 7.2 (2009): 322-334. <http://eudml.org/doc/269183>.

@article{MariellaCecchi2009,
abstract = {A characterization of oscillation and nonoscillation of the Emden-Fowler difference equation \[ \Delta (a\_n \left| \{\Delta x\_n \} \right|^\alpha sgn\Delta x\_n ) + b\_n \left| \{x\_\{n + 1\} \} \right|^\beta sgnx\_\{n + 1\} = 0 \] is given, jointly with some asymptotic properties. The problem of the coexistence of all possible types of nonoscillatory solutions is also considered and a comparison with recent analogous results, stated in the half-linear case, is made.},
author = {Mariella Cecchi, Zuzana Došlá, Mauro Marini},
journal = {Open Mathematics},
keywords = {Emden-Fowler type difference equation; Oscillation; Nonoscillation; Reciprocal principle; Emden-Fowler difference equation; oscillation; nonoscillation; reciprocal principle},
language = {eng},
number = {2},
pages = {322-334},
title = {On oscillation and nonoscillation properties of Emden-Fowler difference equations},
url = {http://eudml.org/doc/269183},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Mariella Cecchi
AU - Zuzana Došlá
AU - Mauro Marini
TI - On oscillation and nonoscillation properties of Emden-Fowler difference equations
JO - Open Mathematics
PY - 2009
VL - 7
IS - 2
SP - 322
EP - 334
AB - A characterization of oscillation and nonoscillation of the Emden-Fowler difference equation \[ \Delta (a_n \left| {\Delta x_n } \right|^\alpha sgn\Delta x_n ) + b_n \left| {x_{n + 1} } \right|^\beta sgnx_{n + 1} = 0 \] is given, jointly with some asymptotic properties. The problem of the coexistence of all possible types of nonoscillatory solutions is also considered and a comparison with recent analogous results, stated in the half-linear case, is made.
LA - eng
KW - Emden-Fowler type difference equation; Oscillation; Nonoscillation; Reciprocal principle; Emden-Fowler difference equation; oscillation; nonoscillation; reciprocal principle
UR - http://eudml.org/doc/269183
ER -

References

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  2. [2] Cecchi M., Došlá Z., Marini M., Nonoscillatory half-linear difference equations and recessive solutions, Adv. Difference Equ., 2005, 2, 193–204 http://dx.doi.org/10.1155/ADE.2005.193[Crossref] Zbl1111.39005
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