Existence of Positive Solutions for a class of Quasilinear Schr\"{o}dinger Equations of Choquard type

In this paper, we study the following quasilinear Schr"{o}dinger equation of Choquard type $$-\mathrm{△}u+V(x)u-\mathrm{△}(u^2)u=(I_{\alpha }\ast \mathrm{\mid }u{\mathrm{\mid }}^p)\mathrm{\mid }u{\mathrm{\mid }}^{p-2}u,x\in {\mathbb{R}}^N,$$ where $N\ge 3$,\ $0<\alpha <N$, $\frac{2(N+\alpha )}{N}\le p<\frac{2(N+\alpha )}{N-2}$ and $I_{\alpha }$ is a Riesz potential. Under appropriate assumptions on $V(x)$, we establish the existence of positive solutions.