| Title:
|
On the existence of solutions of some second order nonlinear difference equations (English) |
| Author:
|
Migda, Małgorzata |
| Author:
|
Schmeidel, Ewa |
| Author:
|
Zbąszyniak, Małgorzata |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
379-388 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a second order nonlinear difference equation \[ \Delta ^2 y_n = a_n y_{n+1} + f(n,y_n,y_{n+1})\,,\quad n\in N\,. \qquad \mathrm {(\mbox{E})}\] The necessary conditions under which there exists a solution of equation (E) which can be written in the form \[ y_{n+1} = \alpha _{n}{u_n} + \beta _{n}{v_n}\,,\quad \mbox{are given.} \] Here $u$ and $v$ are two linearly independent solutions of equation \[ \Delta ^2 y_n = a_{n+1} y_{n+1}\,, \quad ({\lim \limits _{n \rightarrow \infty } \alpha _{n} = \alpha <\infty } \quad {\rm and} \quad {\lim \limits _{n \rightarrow \infty } \beta _{n} = \beta <\infty })\,. \] A special case of equation (E) is also considered. (English) |
| Keyword:
|
nonlinear difference equation |
| Keyword:
|
nonoscillatory solution |
| Keyword:
|
second order |
| MSC:
|
39A10 |
| MSC:
|
39A11 |
| idZBL:
|
Zbl 1122.39001 |
| idMR:
|
MR2195491 |
| . |
| Date available:
|
2008-06-06T22:46:36Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107967 |
| . |
| 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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