Singular anisotropic equations with a sign-changing perturbation

We consider an anisotropic Dirichlet problem driven by the variable (p, q)-Laplacian (double phase problem). In the reaction, we have the competing effects of a singular term and of a superlinear perturbation. Contrary to most of the previous papers, we assume that the perturbation changes sign. We prove a multiplicity result producing two positive smooth solutions when the coefficient function in the singular term is small in the L∞-norm.