| Title:
|
Regular half-linear second order differential equations (English) |
| Author:
|
Došlý, Ondřej |
| Author:
|
Řezníčková, Jana |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
233-245 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the concept of the regular (nonoscillatory) half-linear second order differential equation \[ \left(r(t)\Phi (x^{\prime })\right)^{\prime }+c(t)\Phi (x)=0\,,\quad \Phi (x):=|x|^{p-2}x\,,\quad p>1 \qquad \mathrm {{(*)}}\] and we show that if (*) is regular, a solution $x$ of this equation such that $x^{\prime }(t)\ne 0$ for large $t$ is principal if and only if \[ \int ^\infty \frac{dt}{r(t)x^2(t)|x^{\prime }(t)|^{p-2}}=\infty \,. \] Conditions on the functions $r,c$ are given which guarantee that (*) is regular. (English) |
| Keyword:
|
regular half-linear equation |
| Keyword:
|
principal solution |
| Keyword:
|
Picone’s identity |
| Keyword:
|
Riccati-type equation |
| MSC:
|
34C10 |
| idZBL:
|
Zbl 1119.34029 |
| idMR:
|
MR2010724 |
| . |
| Date available:
|
2008-06-06T22:41:58Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107870 |
| . |
| 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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| . |
