Parametric anisotropic singular equations with [p(z), q(z)]-growth conditions and indefinite perturbation

We study a parametric, anisotropic, singular equation with a reaction which has the combined effects of a singular term and of a superlinear perturbation which can be sign-changing. Using variational tools together with truncation and comparison techniques, we prove an existence and multiplicity result which is global with respect to the parameter (a “bifurcation-type" theorem).