Multiplicity and concentration behaviour of solutions for a fractional Choquard equation with critical growth

Abstract In this paper, we study the singularly perturbed fractional Choquard equation ε2s(−Δ)su+V(x)u=εμ−3(∫R3|u(y)|2μ,s∗+F(u(y))|x−y|μdy)(|u|2μ,s∗−2u+12μ,s∗f(u))inR3, $$\begin{equation*}\varepsilon^{2s}(-{\it\Delta})^su+V(x)u=\varepsilon^{\mu-3}(\int\li

**摘要** 在本文中，我们研究了奇异摄动分数阶Choquard方程 \(\varepsilon^{2s}(-\Delta)^su + V(x)u=\varepsilon^{\mu - 3}\left(\int_{\mathbb{R}^3}\frac{|u(y)|^{2\mu,s*}+F(u(y))}{|x - y|^{\mu}}dy\right)(|u|^{2\mu,s*}-2u+\frac{1}{2\mu,s*}f(u))\)在\(\mathbb{R}^3\)中， （注：其中一些符号如\(2\mu,s*\)不太明确其确切含义，可能是特定领域的特定定义符号）