Liouville‐type theorems for a nonlinear fractional Choquard equation

Anh Tuan Duong, Tran Thi Loan, Dao Trong Quyet and Dao Manh Thang

Mathematische Nachrichten, 2023, vol. 296, issue 6, 2321-2331

Abstract: In this paper, we are concerned with the fractional Choquard equation on the whole space RN$\mathbb {R}^N$(−Δ)su=1|x|N−2s∗upup−1$$\begin{equation*} \hspace*{7pc}(-\Delta )^s u={\left(\frac{1}{|x|^{N-2s}}*u^p\right)}u^{p-1} \end{equation*}$$with 0 2s$N>2s$ and p∈R$p\in \mathbb {R}$. We first prove that the equation does not possess any positive solution for p≤1$p\le 1$. When p>1$p>1$, we establish a Liouville type theorem saying that if N

Date: 2023
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