Geodesic
Positive solutions of nonlinear elliptic equations in a half space in \(\mathbb{R}^2\)
Electronic journal of differential equations, Tome 2002 (2002)
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__a72,
     author = {Bachar,  Imed and M\^aagli,  Habib and M\^aatoug,  Lamia},
     title = {Positive solutions of nonlinear elliptic equations in a half space in {\(\mathbb{R}^2\)}},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {0995.31003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a72/}
}
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%F EJDE_2002__2002__a72
Bachar,  Imed; Mâagli,  Habib; Mâatoug,  Lamia. Positive solutions of nonlinear elliptic equations in a half space in \(\mathbb{R}^2\). Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a72/