Electron. J. Diff. Eqns., Vol. 2002(2002), No. 41, pp. 1-24.

Positive solutions of nonlinear elliptic equations in a half space in $\mathbb{R}^2$

Imed Bachar, Habib Maagli, & Lamia Maatoug

Abstract:
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.

Submitted December 14, 2001. Published May 16, 2002.
Math Subject Classifications: 31A25, 31A35, 34B15, 34B27, 35J65.
Key Words: Singular elliptic equation, superharmonic function, Green function, Schauder fixed point theorem, maximun principle.

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Imed Bachar
Departement de Mathematiques
Faculte des Sciences de Tunis
Campus universitaire 1060 Tunis, Tunisia
e-mail: Imed.Bachar@ipeigb.rnu.tn
Habib Maagli
Departement de Mathematiques
Faculte des Sciences de Tunis
Campus universitaire 1060 Tunis, Tunisia
e-mail: habib.maagli@fst.rnu.tn
Lamia Maatoug
Departement de Mathematiques
Faculte des Sciences de Tunis
Campus universitaire 1060 Tunis, Tunisia
e-mail: Lamia.Maatoug@ipeit.rnu.tn

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