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Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions

Singularly perturbed Choquard equations with nonlinearity satisfying Berestycki-Lions assumptions

Abstract In the present paper, we consider the following singularly perturbed problem: $$\begin{array}{} \displaystyle \left\{ \begin{array}{ll} -\varepsilon^2\triangle u+V(x)u=\varepsilon^{-\alpha}(I_{\alpha}*F(u))f(u), & x\in \mathbb{R}^N; \\ u\in H^1(\mathbb{R}^N), \end{array} \right. \end{array}$$ where ε > 0 is a parameter, N ≥ 3, α ∈ (0, N ), F ( t ) = $\begin{array}{} \int_{0}^{t} \end{array}$ …