Geodesic
A nonlinear differential equation involving reflection of the argument
Archivum mathematicum, Tome 40 (2004) no. 1, pp. 63-68.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
Classification : 34B15
Keywords: reflection; Brouwer fixed point; Kirchhoff equation 
@article{ARM_2004__40_1_a6,
     author = {Ma, T. F. and Miranda, E. S. and de Souza Cortes, M. B.},
     title = {A nonlinear differential equation involving reflection of the argument},
     journal = {Archivum mathematicum},
     pages = {63--68},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {2004},
     mrnumber = {2054873},
     zbl = {1116.34309},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2004__40_1_a6/}
}
TY  - JOUR
AU  - Ma, T. F.
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
SP  - 63
EP  - 68
VL  - 40
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ARM_2004__40_1_a6/
LA  - en
ID  - ARM_2004__40_1_a6
ER  - 
%0 Journal Article
%A Ma, T. F.
%A Miranda, E. S.
%A de Souza Cortes, M. B.
%T A nonlinear differential equation involving reflection of the argument
%J Archivum mathematicum
%D 2004
%P 63-68
%V 40
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ARM_2004__40_1_a6/
%G en
%F ARM_2004__40_1_a6
Ma, T. F.; Miranda, E. S.; de Souza Cortes, M. B. A nonlinear differential equation involving reflection of the argument. Archivum mathematicum, Tome 40 (2004) no. 1, pp. 63-68. http://geodesic.mathdoc.fr/item/ARM_2004__40_1_a6/