Existence results for some anisotropic possible singular problems via the sub-supersolution method

Using the sub-super solution method, we prove the existence of the solutions for the following anisotropic problem with singularity: $$\begin{cases} -\sum\limits_{i=1}^{N} \partial_{i} \left({| \partial_{i} u \vert}^{p_{i}-2} \partial_{i} u \right) = f(x,u) &\qquad\text{in $\;\;\Omega$,}\\ u>0 &\qquad\text{in $\;\;\Omega $,}\\ u=0 &\qquad\text{on $\;\;\partial\Omega $,} \end{cases}$$ where $\Omega \subset \mathbb{R}^{N} $ is a bounded domain with smooth boundary and a given singular nonlinearity $f:\Omega\times(0,\infty)\longrightarrow [0,\infty)$.