Semilinear degenerate elliptic equation in the presence of singular nonlinearity

Given $\mathrm{\Omega }(\subseteq R^{1+m})$, a smooth bounded domain and a nonnegative measurable function $f$ defined on $\mathrm{\Omega }$ with suitable summability. In this paper, we will study the existence and regularity of solutions to the quasilinear degenerate elliptic equation with a singular nonlinearity given by: \begin{align} -Δ_λu&=\frac{f}{u^ν} $\text{ in }$Ω\nonumber &u>0 $\text{ in }$ Ω\nonumber &u=0 $\text{ on }$ \partialΩ\nonumber \end{align} where the operator ${\mathrm{\Delta }}_{\lambda }$ is given by $${\mathrm{\Delta }}_{\lambda }u=u_{xx}+\mathrm{\mid }x{\mathrm{\mid }}^{2\lambda }{\mathrm{\Delta }}_{y}u;(x,y)\in R\times R^m$$ is known as the Grushin operator.