Liouville‐type theorems for a nonlinear fractional Choquard equation

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 01$, we establish a Liouville type theorem saying that...

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Bibliographic Details
Published in:Mathematische Nachrichten 2023-06, Vol.296 (6), p.2321-2331
Main Authors: Duong, Anh Tuan, Loan, Tran Thi, Quyet, Dao Trong, Thang, Dao Manh
Format: Article
Language:English
Subjects:
fractional Choquard equations
Liouville theorem
Liouville‐type theorems
stable solutions
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Summary: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 01$, we establish a Liouville type theorem saying that if N
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202000462