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In the present paper, we consider the following singularly perturbed problem:    $$ \textstyle\begin{cases} -\varepsilon ^{2}\Delta u+V(x)u-\varepsilon ^{2}\Delta (u^{2})u= \varepsilon ^{-\alpha }(I_{\alpha }*G(u))g(u), \quad x\in \mathbb{R}^{N}; \\ u\in H^{1}(\mathbb{R}^{N}), \end{cases} $$  { − ε 2 Δ u + V ( x ) u − ε 2 Δ ( u 2 ) u = ε − α ( I α ∗ G ( u ) ) g ( u ) , x ∈ R N ; u ∈ H 1 ( R N ) , where    $\varepsilon &gt;0$  ε &gt; 0 is a parameter,    $N\ge 3$  N ≥ 3 ,    $\alpha \in (0, N)$  α ∈ ( 0 , N ) ,    $G(t)=\int _{0}^{t}g(s)\,\mathrm{d}s$  G ( t ) = ∫ 0 t g ( s ) d s ,    $I_{\alpha }: \mathbb{R}^{N}\rightarrow \mathbb{R}$  I α : R N → R is the Riesz potential, and    $V\in \mathcal{C}(\mathbb{R}^{N}, \mathbb{R})$  V ∈ C ( R N , R ) with    $0&lt;\min_{x\in \mathbb{R}^{N}}V(x)&lt; \lim_{|y|\to \infty }V(y)$  0 &lt; min x ∈ R N V ( x ) &lt; lim | y | → ∞ V ( y ) . Under the general Berestycki–Lions assumptions on  g , we prove that there exists a constant    $\varepsilon _{0}&gt;0$  ε 0 &gt; 0 determined by  V  and  g  such that for    $\varepsilon \in (0,\varepsilon _{0}]$  ε ∈ ( 0 , ε 0 ] the above problem admits a semiclassical ground state solution    $\hat{u}_{\varepsilon }$  u ˆ ε with exponential decay at infinity. We also study the asymptotic behavior of    $\{\hat{u}_{\varepsilon }\}$  { u ˆ ε } as    $\varepsilon \to 0$  ε → 0 .

Singularly perturbed quasilinear Choquard equations with nonlinearity satisfying Berestycki–Lions assumptions