A nonlinear differential equation involving reflection of the argument
Ma, To Fu ; Miranda, E. S. ; de Souza Cortes, M. B.
Archivum Mathematicum, Tome 040 (2004), p. 63-68 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2004-01-01
Classification:  34B15 
@article{107891,
     author = {To Fu Ma and E. S. Miranda and M. B. de Souza Cortes},
     title = {A nonlinear differential equation involving reflection of the argument},
     journal = {Archivum Mathematicum},
     volume = {040},
     year = {2004},
     pages = {63-68},
     zbl = {1116.34309},
     mrnumber = {2054873},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107891}
}

Ma, To Fu; Miranda, E. S.; de Souza Cortes, M. B. A nonlinear differential equation involving reflection of the argument. Archivum Mathematicum, Tome 040 (2004) pp. 63-68. http://gdmltest.u-ga.fr/item/107891/

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