| Title:
|
Some properties of third order differential operators (English) |
| Author:
|
Cecchi, M. |
| Author:
|
Došlá, Z. |
| Author:
|
Marini, M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
729-748 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Consider the third order differential operator $L$ given by \[L(\cdot )\equiv \,\frac {1}{a_3(t)}\frac {\mbox{d}}{\mbox{d} t}\frac {1}{a_2(t)}\frac {\mbox{d}}{\mbox{d} t} \frac {1}{a_1(t)}\frac {\mbox{d}}{\mbox{d} t}\,(\cdot ) \] and the related linear differential equation $L(x)(t)+x(t)=0$. We study the relations between $L$, its adjoint operator, the canonical representation of $L$, the operator obtained by a cyclic permutation of coefficients $a_i$, $ i=1,2,3$, in $L$ and the relations between the corresponding equations. We give the commutative diagrams for such equations and show some applications (oscillation, property A). (English) |
| Keyword:
|
Differential operators |
| Keyword:
|
linear differential equation of third order |
| Keyword:
|
canonical forms |
| Keyword:
|
adjoint equation |
| Keyword:
|
cyclic permutation |
| Keyword:
|
oscillatory solution |
| Keyword:
|
Kneser solution |
| Keyword:
|
property $\mathrm A$ |
| MSC:
|
34A30 |
| MSC:
|
34C10 |
| MSC:
|
34C20 |
| idZBL:
|
Zbl 0903.34032 |
| idMR:
|
MR1479316 |
| . |
| Date available:
|
2009-09-24T10:10:07Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127390 |
| . |
| Reference:
|
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