| Title:
|
Strong singularities in mixed boundary value problems (English) |
| Author:
|
Rachůnková, Irena |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
131 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
393-409 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study singular boundary value problems with mixed boundary conditions of the form \[ (p(t)u^{\prime })^{\prime }+ p(t)f(t,u,p(t)u^{\prime })=0, \quad \lim _{t\rightarrow 0+}p(t)u^{\prime }(t)=0, \quad u(T)=0, \] where $[0,T]\subset {\mathbb{R}}.$ We assume that ${\mathbb{R}}^2,$ $f$ satisfies the Carathéodory conditions on $(0,T)\times $ $p\in C[0,T]$ and ${1/p}$ need not be integrable on $[0,T].$ Here $f$ can have time singularities at $t=0$ and/or $t=T$ and a space singularity at $x=0$. Moreover, $f$ can change its sign. Provided $f$ is nonnegative it can have even a space singularity at $y=0.$ We present conditions for the existence of solutions positive on $[0,T).$ (English) |
| Keyword:
|
singular mixed boundary value problem |
| Keyword:
|
positive solution |
| Keyword:
|
lower function |
| Keyword:
|
upper function |
| Keyword:
|
convergence of approximate regular problems |
| MSC:
|
34B15 |
| MSC:
|
34B16 |
| MSC:
|
34B18 |
| idZBL:
|
Zbl 1114.34020 |
| idMR:
|
MR2273930 |
| DOI:
|
10.21136/MB.2006.133975 |
| . |
| Date available:
|
2009-09-24T22:27:43Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133975 |
| . |
| Reference:
|
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