  We report on some recent existence and uniqueness results for elliptic
equations subject to Dirichlet boundary condition and involving a singular
nonlinearity. We take into account the following types of problems: (i)
singular problems with sublinear nonlinearity and two parameters; (ii) combined
effects of asymptotically linear and singular nonlinearities in bifurcation
problems; (iii) bifurcation for a class of singular elliptic problems with
subquadratic convection term. In some concrete situations we also establish the
asymptotic behaviour of the solution around the bifurcation point. Our analysis
relies on the maximum principle for elliptic equations combined with adequate
estimates.
