On positive solutions of quasi-linear elliptic equations (Q1107024)

The author proves the existence of positive solutions of the Dirichlet problem for a quasi-linear elliptic equation, where the nonlinearity f(x,u) satisfies the following two conditions (a) f(x,0)\(\geq 0\), (b) there exist functions \(g\in L^{\infty}\) and \(c\in L^ 2\) such that \(f(x,s)\leq g(x)s+c(x)\) for all \(s\geq 0\). The boundary data belong to \(L^ 2\) and a corresponding solution is in a weighted Sobolev space.