| Title:
|
Singular nonlinear problem for ordinary differential equation of the second order (English) |
| Author:
|
Rachůnková, Irena |
| Author:
|
Tomeček, Jan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
75-84 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the singular nonlinear problem \[ u^{\prime \prime }(t) + f(t,u(t),u^{\prime }(t)) = 0,\quad u(0) = 0,\quad u^{\prime }(T) = \psi (u(T)), \] where $f \in \mathop {\mathit{Car}}((0,T)\times D)$, $D = (0,\infty )\times $. We prove the existence of a solution to this problem which is positive on $(0,T]$ under the assumption that the function $f(t,x,y)$ is nonnegative and can have time singularities at $t = 0$, $t = T$ and space singularity at $x = 0$. The proof is based on the Schauder fixed point theorem and on the method of a priori estimates. (English) |
| Keyword:
|
singular ordinary differential equation of the second order |
| Keyword:
|
lower and upper functions |
| Keyword:
|
nonlinear boundary conditions |
| Keyword:
|
time singularities |
| Keyword:
|
phase singularity |
| MSC:
|
34B15 |
| MSC:
|
34B16 |
| MSC:
|
34B18 |
| idZBL:
|
Zbl 1147.34012 |
| idMR:
|
MR2387495 |
| . |
| Date available:
|
2009-08-27T10:39:16Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133395 |
| . |
| 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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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
