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In this study, we consider the following quasilinear Choquard equation with singularity−Δu+V(x)u−uΔu2+λ(Iα∗∣u∣p)∣u∣p−2u=K(x)u−γ,x∈RN,u&gt;0,x∈RN,\left\{\begin{array}{ll}-\Delta u+V\left(x)u-u\Delta {u}^{2}+\lambda \left({I}_{\alpha }\ast | u{| }^{p})| u{| }^{p-2}u=K\left(x){u}^{-\gamma },\hspace{1.0em}&amp; x\in {{\mathbb{R}}}^{N},\\ u\gt 0,\hspace{1.0em}&amp; x\in {{\mathbb{R}}}^{N},\end{array}\right.whereIα{I}_{\alpha }is a Riesz potential,0&lt;α&lt;N0\lt \alpha \lt N, andN+αN&lt;p&lt;N+αN−2\displaystyle \frac{N+\alpha }{N}\lt p\lt \displaystyle \frac{N+\alpha }{N-2}, withλ&gt;0\lambda \gt 0. Under suitable assumption onVVandKK, we research the existence of positive solutions of the equations. Furthermore, we obtain the asymptotic behavior of solutions asλ→0\lambda \to 0.

Existence and asymptotical behavior of solutions for a quasilinear Choquard equation with singularity