  We consider a Dirichlet elliptic problem driven by the Laplacian with
singular and superlinear nonlinearities. The singular term appears on the
left-hand side while the superlinear perturbation is parametric with parameter
$\lambda>0$ and it need not satisfy the AR-condition. Having as our starting
point the work of Diaz-Morel-Oswald (1987), we show that there is a critical
parameter value $\lambda_*$ such that for all $\lambda>\lambda_*$ the problem
has two positive solutions, while for $\lambda<\lambda_*$ there are no positive
solutions. What happens in the critical case $\lambda = \lambda_*$ is an
interesting open problem.
