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)) is an element of R-2 : x(2) > 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.