In this paper, we study the nonlinear Choquard equation e2s(−Δ)su+V(x)u=Iα*|u|2α,s*|u|2α,s*−2u,u∈Ds,2(RN), where s ∈ (0, 1), N ≥ 3, ɛ is the positive parameter, and 2α,s*=N+αN−2s is the critical exponent with respect to the Hardy–Littlewood–Sobolev inequality. V(x)∈LN2s(RN), where V(x) is assumed to be zero in some region of RN, which means that it is of the critical frequency case. In virtue of a global compactness result in fractional Sobolev space and Lusternik–Schnirelmann theory of critical points, we succeed in proving the multiplicity of bound state solutions.

中文翻译：

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具有 Hardy-Littlewood-Sobolev 临界指数的分数阶 Choquard 方程的多重束缚态解

本文研究非线性Choquard方程e2s(−Δ)su+V(x)u=Iα*|u|2α,s*|u|2α,s*−2u,u∈Ds,2(RN) , 其中 s ∈ (0, 1), N ≥ 3, ɛ 是正参数，2α,s*=N+αN−2s 是关于 Hardy-Littlewood-Sobolev 不等式的临界指数。V(x)∈LN2s(RN)，其中在RN的某个区域假设V(x)为零，这意味着它是临界频率情况。凭借分数 Sobolev 空间和 Lusternik-Schnirelmann 临界点理论的全局紧凑性结果，我们成功地证明了束缚态解的多样性。