Ground state solutions for a quasilinear Schrodinger equation with singular coefficients

In this article, we study the quasilinear Schrodinger equation with the critical exponent and singular coefficients, $$ -\Delta u +V(x)u-\Delta(|u|^2)u=\lambda\frac{|u|^{q-2}u}{|x|^{\mu}} +\frac{|u|^{22^*(\nu)-2}u}{|x|^\nu}\quad\text{in } \mathbb{R}^N, $$ where $N\geq 3$, $2<q<22^*(\mu)$, $2^*(s)=\frac{2(N-s)}{N-2}$, and $\lambda, \mu, \nu$ are parameters with $\lambda>0$, $\mu, \nu \in [0,2)$. By applying the Mountain Pass Theorem and the Concentration Compactness Principle, we establish the existence of the ground state solutions to the above problem