| Title:
|
Non-oscillation of second order linear self-adjoint nonhomogeneous difference equations (English) |
| Author:
|
Parhi, N. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
3 |
| Year:
|
2011 |
| Pages:
|
241-258 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper, conditions are obtained, in terms of coefficient functions, which are necessary as well as sufficient for non-oscillation/oscillation of all solutions of self-adjoint linear homogeneous equations of the form \[ \Delta (p_{n-1}\Delta y_{n-1}) + q y_{n} =0 , \quad n\geq 1, \] where $q$ is a constant. Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of all solutions of nonlinear non-homogeneous equations of the type \[ \Delta (p_{n-1}\Delta y_{n-1}) + q_{n}g( y_{n}) = f_{n-1}, \quad n\geq 1, \] where, unlike earlier works, $f_{n}\geq 0$ or $\leq 0$ (but $\not \equiv 0)$ for large $n$. Further, these results are used to obtain sufficient conditions for non-oscillation of all solutions of forced linear third order difference equations of the form \[ y_{n+2}+ a_{n}y_{n+1}+ b_{n}y_{n}+ c_{n}y_{n-1}= g_{n-1}, \quad n\geq 1. \] (English) |
| Keyword:
|
oscillation |
| Keyword:
|
non-oscillation |
| Keyword:
|
second order difference equation |
| Keyword:
|
third order difference equation |
| Keyword:
|
generalized zero |
| MSC:
|
39A06 |
| MSC:
|
39A10 |
| MSC:
|
39A12 |
| MSC:
|
39A21 |
| idZBL:
|
Zbl 1249.39015 |
| idMR:
|
MR2893974 |
| DOI:
|
10.21136/MB.2011.141647 |
| . |
| Date available:
|
2011-09-22T14:55:17Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141647 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
