| Title:
|
A nonlinear differential equation involving reflection of the argument (English) |
| Author:
|
Ma, T. F. |
| Author:
|
Miranda, E. S. |
| Author:
|
de Souza Cortes, M. B. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
40 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
63-68 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the nonlinear boundary value problem involving reflection of the argument \[ -M\Big (\int _{-1}^1\vert u^{\prime }(s)\vert ^2\,ds\Big )\,u^{\prime \prime }(x) = f\big (x,u(x),u(-x)\big ) \quad \quad x \in [-1,1]\,, \] where $M$ and $f$ are continuous functions with $M>0$. Using Galerkin approximations combined with the Brouwer’s fixed point theorem we obtain existence and uniqueness results. A numerical algorithm is also presented. (English) |
| Keyword:
|
reflection |
| Keyword:
|
Brouwer fixed point |
| Keyword:
|
Kirchhoff equation |
| MSC:
|
34B15 |
| idZBL:
|
Zbl 1116.34309 |
| idMR:
|
MR2054873 |
| . |
| Date available:
|
2008-06-06T22:42:56Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107891 |
| . |
| 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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| . |
