We study the existence, nonexistence and multiplicity of nonnegative solutions for the quasilinear elliptic problem                                                                                                            where Ω is a bounded domain in RN, λ > 0 is a parameter, △p = div(|∇u|p−2∇u) is the p−Laplace operator of u, 1 < p < N, 0 < q < p − 1 < r ≤ p∗ − 1, a(x), b(x) are bounded functions, the coefficient b(x) is assumed to be nonnegative and a(x) is allowed to change sign. The results of the semilinear equations are extended to the quasilinear problem.