A nonlinear differential equation involving reflection of the argument
To Fu Ma; E. S. Miranda; M. B. de Souza Cortes
Archivum Mathematicum (2004)
- Volume: 040, Issue: 1, page 63-68
- ISSN: 0044-8753
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topMa, To Fu, Miranda, E. S., and de Souza Cortes, M. B.. "A nonlinear differential equation involving reflection of the argument." Archivum Mathematicum 040.1 (2004): 63-68. <http://eudml.org/doc/249316>.
@article{Ma2004,
abstract = {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.},
author = {Ma, To Fu, Miranda, E. S., de Souza Cortes, M. B.},
journal = {Archivum Mathematicum},
keywords = {reflection; Brouwer fixed point; Kirchhoff equation; Brouwer fixed point; Kirchhoff equation},
language = {eng},
number = {1},
pages = {63-68},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A nonlinear differential equation involving reflection of the argument},
url = {http://eudml.org/doc/249316},
volume = {040},
year = {2004},
}
TY - JOUR
AU - Ma, To Fu
AU - Miranda, E. S.
AU - de Souza Cortes, M. B.
TI - A nonlinear differential equation involving reflection of the argument
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 1
SP - 63
EP - 68
AB - 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.
LA - eng
KW - reflection; Brouwer fixed point; Kirchhoff equation; Brouwer fixed point; Kirchhoff equation
UR - http://eudml.org/doc/249316
ER -
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