POSITIVE SOLUTIONS FOR NONLINEAR SINGULAR PROBLEMS WITH SIGN-CHANGING NONLINEARITIES

. We consider a Dirichlet problem driven by a general nonlinear, nonhomogeneous differential operator. The reaction has the competing effects of a singular term and of a parametric perturbation which is superlinear and sign-changing. Using variational tools from critical point theory together with truncation and comparison techniques, we show that for all small values of the parameter, the problem has at least two positive smooth solutions. Also, we show the existence of a smallest positive solution (minimal positive solution).