Oscillation properties for a scalar linear difference equation of mixed type

Leonid Berezansky; Sandra Pinelas

Mathematica Bohemica (2016)

  • Volume: 141, Issue: 2, page 169-182
  • ISSN: 0862-7959

Abstract

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The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type Δ x ( n ) + ∑ k = - p q a k ( n ) x ( n + k ) = 0 , n > n 0 , where Δ x ( n ) = x ( n + 1 ) - x ( n ) is the difference operator and { a k ( n ) } are sequences of real numbers for k = - p , ... , q , and p > 0 , q ≥ 0 . We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced.

How to cite

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Berezansky, Leonid, and Pinelas, Sandra. "Oscillation properties for a scalar linear difference equation of mixed type." Mathematica Bohemica 141.2 (2016): 169-182. <http://eudml.org/doc/276983>.

@article{Berezansky2016,
abstract = {The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type \[ \Delta x(n)+\sum \_\{k=-p\}^\{q\}a\_\{k\}(n)x(n+k)=0,\quad n>n\_\{0\}, \] where $\Delta x(n)=x(n+1)-x(n)$ is the difference operator and $\lbrace a_\{k\}(n)\rbrace $ are sequences of real numbers for $k=-p,\ldots ,q$, and $p>0$, $q\ge 0$. We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced.},
author = {Berezansky, Leonid, Pinelas, Sandra},
journal = {Mathematica Bohemica},
keywords = {oscillation; difference equation; mixed type; asymptotic behavior},
language = {eng},
number = {2},
pages = {169-182},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation properties for a scalar linear difference equation of mixed type},
url = {http://eudml.org/doc/276983},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Berezansky, Leonid
AU - Pinelas, Sandra
TI - Oscillation properties for a scalar linear difference equation of mixed type
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 2
SP - 169
EP - 182
AB - The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type \[ \Delta x(n)+\sum _{k=-p}^{q}a_{k}(n)x(n+k)=0,\quad n>n_{0}, \] where $\Delta x(n)=x(n+1)-x(n)$ is the difference operator and $\lbrace a_{k}(n)\rbrace $ are sequences of real numbers for $k=-p,\ldots ,q$, and $p>0$, $q\ge 0$. We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced.
LA - eng
KW - oscillation; difference equation; mixed type; asymptotic behavior
UR - http://eudml.org/doc/276983
ER -

References

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