Multiple Ordered Positive Solutions of an Elliptic Problem Involving the p&q-Laplacian

We are concerned with questions of existence and multiplicity of positive solutions of the elliptic problem $$\left\{\begin{array}{rclcc} -\mathrm{div} \;(\mathcal{K}(|\nabla u|^{p})|\nabla u|^{p-2}\nabla u) & = & \lambda f(u) & \text{in} & \Omega, \\ u & = & 0 & \text{on}& \partial\Omega \end{array} \right. \tag{$P_{\lambda}$}$$ with $1<p<\infty$, where $\Omega \subset \mathbb{R}^{N}$ is a bounded smooth domain, $\lambda$ is a positive real parameter, $\mathcal{K}:\mathbb{R}^{+}\rightarrow \mathbb{R}^{+}$ is a $C^{1}$-function and $f:\mathbb{R}\rightarrow \mathbb{R}$ is a continuous functions which changes sign. We use variational methods.