| Title:
|
On Existence and Asymptotic Properties of Kneser Solutions to Singular Second Order ODE. (English) |
| Author:
|
Vampolová, Jana |
| Language:
|
English |
| Journal:
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Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
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0231-9721 |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
135-152 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate an asymptotic behaviour of damped non-oscillatory solutions of the initial value problem with a time singularity $\left( p(t)u^{\prime }(t) \right)^{\prime } + p(t)f ( u(t) )=0$, $u(0)=u_0$, $u^{\prime }(0)=0$ on the unbounded domain $[0,\infty )$. Function $f$ is locally Lipschitz continuous on $\mathbb {R}$ and has at least three zeros $L_0 <0$, $0$ and $L>0$. The initial value $u_0\in (L_0, L)\setminus \lbrace 0\rbrace $. Function $p$ is continuous on $[0,\infty ),$ has a positive continuous derivative on $(0,\infty )$ and $p(0)=0$. Asymptotic formulas for damped non-oscillatory solutions and their first derivatives are derived under some additional assumptions. Further, we provide conditions for functions $p$ and $f$, which guarantee the existence of Kneser solutions. (English) |
| Keyword:
|
singular ordinary differential equation of the second order |
| Keyword:
|
time singularities |
| Keyword:
|
unbounded domain |
| Keyword:
|
asymptotic properties |
| Keyword:
|
Kneser solutions |
| Keyword:
|
damped solutions |
| Keyword:
|
non-oscillatory solutions |
| MSC:
|
34A12 |
| MSC:
|
34D05 |
| idZBL:
|
Zbl 06285760 |
| idMR:
|
MR3202755 |
| . |
| Date available:
|
2013-08-02T08:05:21Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143397 |
| . |
| Reference:
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