| Title:
|
On small solutions of second order differential equations with random coefficients (English) |
| Author:
|
Hatvani, László |
| Author:
|
Stachó, László |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
119-126 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the equation \[x^{\prime \prime }+a^2(t)x=0,\qquad a(t):=a_k\ \hbox{ if }t_{k-1}\le t<t_k,\ \hbox{ for }k=1,2,\ldots ,\] where $\lbrace a_k\rbrace $ is a given increasing sequence of positive numbers, and $\lbrace t_k\rbrace $ is chosen at random so that $\lbrace t_k-t_{k-1}\rbrace $ are totally independent random variables uniformly distributed on interval $[0,1]$. We determine the probability of the event that all solutions of the equation tend to zero as $t\rightarrow \infty $. (English) |
| Keyword:
|
Asymptotic stability |
| Keyword:
|
energy method |
| Keyword:
|
small solution |
| MSC:
|
34D20 |
| MSC:
|
34F05 |
| MSC:
|
60H10 |
| MSC:
|
60K40 |
| idZBL:
|
Zbl 0915.34051 |
| idMR:
|
MR1629680 |
| . |
| Date available:
|
2009-02-17T10:10:41Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107638 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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