  We study the existence of positive solutions for a class of double phase
Dirichlet equations which have the combined effects of a singular term and of a
parametric superlinear term. The differential operator of the equation is the
sum of a $p$-Laplacian and of a weighted $q$-Laplacian ($q<p$) with
discontinuous weight. Using the Nehari method, we show that for all small
values of the parameter $\lambda>0$, the equation has at least two positive
solutions.
