  We consider a parametric Dirichlet problem driven by the anisotropic
$(p,q)$-Laplacian and with a reaction which exhibits the combined effects of a
superlinear (convex) term and of a negative sublinear term. Using variational
tools and critical groups we show that for all small values of the parameter,
the problem has at least three nontrivial smooth solutions, two of which are of
constant sign (positive and negative).
