| Title:
|
On the oscillation of solutions of third order linear difference equations of neutral type (English) |
| Author:
|
Andruch-Sobiło, Anna |
| Author:
|
Migda, Małgorzata |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
19-33 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we consider the third order linear difference equations of neutral type \[ \Delta ^{3}[x(n)-p(n)x(\sigma (n))]+\delta q(n)x(\tau (n))=0, \quad n \in N(n_0), \qquad \mathrm{({\mathrm E})}\] where $\delta =\pm 1$, $p,q\: N(n_0)\rightarrow \mathbb R_+;$ $\sigma ,\tau \: N(n_0)\rightarrow \mathbb N$, $\lim _{n \rightarrow \infty }\sigma (n)= \lim \limits _{n \rightarrow \infty }\tau (n)= \infty .$ We examine the following two cases: \[ \BOF\align \lbrace 0<p(n)&\le 1, \ \sigma (n)=n+k,\ \tau (n)=n+l\rbrace , \lbrace p(n)&>1, \ \sigma (n)=n-k,\ \tau (n)=n-l\rbrace , \BOF\endalign \] where $k$, $l$ are positive integers and we obtain sufficient conditions under which all solutions of the above equations are oscillatory. (English) |
| Keyword:
|
neutral type difference equation |
| Keyword:
|
nonoscillatory solution |
| Keyword:
|
asymptotic behavior |
| Keyword:
|
oscillation |
| Keyword:
|
third order linear difference equations |
| MSC:
|
39A11 |
| idZBL:
|
Zbl 1110.39002 |
| idMR:
|
MR2128356 |
| DOI:
|
10.21136/MB.2005.134217 |
| . |
| Date available:
|
2009-09-24T22:17:37Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134217 |
| . |
| Reference:
|
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