| Title:
|
Singular Dirichlet problem for ordinary differential equations with $\phi$-Laplacian (English) |
| Author:
|
Polášek, Vladimír |
| Author:
|
Rachůnková, Irena |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
409-425 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We provide sufficient conditions for solvability of a singular Dirichlet boundary value problem with $$-Laplacian \[ \BOF\unknown. ((u^{\prime }))^{\prime } = f(t, u, u^{\prime }), u(0) = A, \ u(T) = B, \BOF\unknown. \] where $$ is an increasing homeomorphism, $(\mathbb{R})=\mathbb{R}$, $(0)=0$, $f$ satisfies the Carathéodory conditions on each set $[a, b]\times \mathbb{R}^{2}$ with $[a, b]\subset (0, T)$ and $f$ is not integrable on $[0, T]$ for some fixed values of its phase variables. We prove the existence of a solution which has continuous first derivative on $[0, T]$. (English) |
| Keyword:
|
singular Dirichlet problem |
| Keyword:
|
$$-Laplacian |
| Keyword:
|
existence of smooth solution |
| Keyword:
|
lower and upper functions |
| MSC:
|
34B15 |
| MSC:
|
34B16 |
| idZBL:
|
Zbl 1114.34017 |
| idMR:
|
MR2182386 |
| DOI:
|
10.21136/MB.2005.134206 |
| . |
| Date available:
|
2009-09-24T22:22:56Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134206 |
| . |
| Reference:
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