| Title:
|
Integral averages and oscillation of second order sublinear differential equations (English) |
| Author:
|
Manojlović, Jelena V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
41-60 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
New oscillation criteria are given for the second order sublinear differential equation \[ [a(t)\psi (x(t))x^{\prime }(t)]^{\prime }+q(t)f(x(t))=0, \quad t\ge t_0>0, \] where $a\in C^1([t_0,\infty ))$ is a nonnegative function, $\psi , f\in C({\mathbb R})$ with $\psi (x)\ne 0$, $xf(x)/\psi (x)>0$ for $x\ne 0$, $\psi $, $f$ have continuous derivative on ${\mathbb R}\setminus \lbrace 0\rbrace $ with $[f(x)/\psi (x)]^{\prime }\ge 0$ for $x\ne 0$ and $q\in C([t_0,\infty ))$ has no restriction on its sign. This oscillation criteria involve integral averages of the coefficients $q$ and $a$ and extend known oscillation criteria for the equation $x^{\prime \prime }(t)+q(t)x(t)=0$. (English) |
| Keyword:
|
oscillation |
| Keyword:
|
sublinear differential equation |
| Keyword:
|
integral averages |
| MSC:
|
34C10 |
| MSC:
|
34C15 |
| MSC:
|
34C29 |
| idZBL:
|
Zbl 1081.34032 |
| idMR:
|
MR2121655 |
| . |
| Date available:
|
2009-09-24T11:20:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127958 |
| . |
| Reference:
|
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