Semilinear elliptic equations with singular nonlinearities

We prove existence, regularity and nonexistence results for problems whose model is -Lambda u = f(x)/u gamma in Omega, with zero Dirichlet conditions on the boundary of an open, bounded subset Omega of R(N). Here gamma > 0 and f is a nonnegative function on Omega. Our results will depend on the summability of f in some Lebesgue spaces, and on the values of gamma (which can be equal, larger or smaller than 1)