Geodesic
Positive solutions of nonlinear elliptic equations in a half space in $\bbfR^2$
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the existence and the asymptotic behaviour of positive solutions of the nonlinear equation $\Delta u+f(.,u)=0$, in the domain $D=\{(x_1,x_2)\in \mathbb{R}^2:x_2 greater than 0\}$, with $u=0$ on the boundary. The aim is to prove some existence results for the above equation in a general setting by using a fixed-point argument.
Classification : 31A25, 31A35, 34B15, 34B27, 35J65
Keywords: singular elliptic equation, superharmonic function, Green function, Schauder fixed point theorem, maximun principle 
@article{EJDE_2002__2002__a272,
     author = {Bachar, Imed and M\^aagli, Habib and M\^aatoug, Lamia},
     title = {Positive solutions of nonlinear elliptic equations in a half space in $\bbfR^2$},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a272/}
}
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Bachar, Imed; Mâagli, Habib; Mâatoug, Lamia. Positive solutions of nonlinear elliptic equations in a half space in $\bbfR^2$. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a272/