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Given $\Omega(\subseteq\;R^{1+m})$, a smooth bounded domain and a nonnegativemeasurable function $f$ defined on $\Omega$ with suitable summability. In thispaper, we will study the existence and regularity of solutions to thequasilinear degenerate elliptic equation with a singular nonlinearity given by:\begin{align} -\Delta_\lambda u&=\frac{f}{u^{\nu}} \text{ in }\Omega\nonumber&u>0 \text{ in } \Omega\nonumber &u=0 \text{ on } \partial\Omega\nonumber\end{align} where the operator $\Delta_\lambda$ is given by$$\Delta_\lambda{u}=u_{xx}+|x|^{2\lambda}\Delta_y{u};\,(x,y)\in \;R\times\;R^m$$ is known as the Grushin operator.

Semilinear degenerate elliptic equation in the presence of singular nonlinearity