  This paper is concerned with the study of multiple positive solutions to the
following elliptic problem involving a nonhomogeneous operator with nonstandard
growth of $p$-$q$ type and singular nonlinearities \begin{equation*}
  \left\{
  \begin{alignedat}{2}
  {} - \mathcal{L}_{p,q} u
  & {}= \lambda \frac{f(u)}{u^\gamma}, \ u>0
  && \quad\mbox{ in } \, \Omega,
  u & {}= 0
  && \quad\mbox{ on } \partial\Omega,
  \end{alignedat}
  \right. \end{equation*} where $\Omega$ is a bounded domain in $\mathbb{R}^N$
with $C^2$ boundary, $N \geq 1$, $\lambda >0$ is a real parameter,
$$\mathcal{L}_{p,q} u := div(|\nabla u|^{p-2} \nabla u + |\nabla u|^{q-2}
\nabla u),$$ $1<p<q< \infty$, $\gamma \in (0,1)$, and $f$ is a continuous
nondecreasing map satisfying suitable conditions. By constructing two
distinctive pairs of strict sub and super solution, and using fixed point
theorems by Amann , we prove existence of three positive solutions in the
positive cone of $C_\delta(\overline{\Omega})$ and in a certain range of
$\lambda$.
