Nonhomogeneous singular problems with sign-changing perturbation

We consider a nonlinear elliptic Dirichlet problem driven by a nonhomogeneous differential operator. In the reaction, we have the combined effects of a parametric singular term plus a (p-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(p-1)$$\end{document}-superlinear perturbation. We do not assume that the perturbation is positive, not even locally at 0+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<^>+$$\end{document}. This is in sharp contrast to all previous works in the literature. We prove an existence and multiplicity theorem which is global in the parameter (a bifurcation-type theorem).