| Title:
|
Oscillation and nonoscillation of higher order self-adjoint differential equations (English) |
| Author:
|
Došlý, Ondřej |
| Author:
|
Osička, Jan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
833-849 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation \[ (-1)^n(t^{\alpha }y^{(n)})^{(n)}+q(t)y=0 \qquad \mathrm{(*)}\] are established. In these criteria, equation $(*)$ is viewed as a perturbation of the conditionally oscillatory equation \[ (-1)^n(t^{\alpha }y^{(n)})^{(n)}- \frac{\mu _{n,\alpha }}{t^{2n-\alpha }}y=0, \] where $\mu _{n,\alpha }$ is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed. (English) |
| Keyword:
|
self-adjoint differential equation |
| Keyword:
|
oscillation and nonoscillation criteria |
| Keyword:
|
variational method |
| Keyword:
|
conditional oscillation |
| MSC:
|
34B05 |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 1023.34028 |
| idMR:
|
MR1940063 |
| . |
| Date available:
|
2009-09-24T10:57:15Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127768 |
| . |
| Reference:
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| Reference:
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