Existence of multiple solutions for a singular and quasilinear equation

In this paper, we study the following singular elliptic problem:where be a bounded smooth domain, denotes the -Laplace operator, is a parameter and is a constant. We require to satisfy assumptions (g1)–(g2) and to satisfy assumptions (h1)–(h4) in Section 1. We employ variational methods in order to show the existence of such that admits at least two solutions for all one solution for and no solution for all