Regularizing Effect in Singular Semilinear Problems

We analyze how different relations in the lower order terms lead to the same regularizing effect on singular problems whose model is-triangle u+ g(x, u) = f (x)/u(gamma) in Omega, u = 0 on partial derivative Omega, where Omega is a bounded open set of R-N, gamma > 0, f (x) is a nonnegative function in L-1(Omega) and g(x, s) is a Caratheodory function. In a framework where no H-0(1) (Omega) solution is expected, we prove its existence (regularizing effect) whenever the datum f interacts conveniently either with the boundary of the domain or with the lower order term.