1. On stable solutions of a weighted elliptic equation involving the fractional Laplacian.
- Author
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Quynh Nguyen, Thi and Tuan Duong, Anh
- Subjects
- *
ELLIPTIC equations , *LAPLACIAN operator , *LIOUVILLE'S theorem , *MATHEMATICS - Abstract
In this paper, we study the following fractional Choquard equation with weight (−Δ)su=1|x|N−α∗h(x)|u|ph(x)|u|p−2uinℝN,$$ {\left(-\Delta \right)}^su=\left(\frac{1}{{\left|x\right|}^{N-\alpha }}\ast h(x){\left|u\right|}^p\right)h(x){\left|u\right|}^{p-2}u\kern0.5em \mathrm{in}\kern0.5em {\mathrm{\mathbb{R}}}^N, $$where 0
2s,p>2,α>0$$ 02s,p>2,\alpha >0 $$ and h$$ h $$ is a positive weight function satisfying h(x)≥C|x|a$$ h(x)\ge C{\left|x\right|}^a $$ at infinity, for some a≥0$$ a\ge 0 $$. We establish, in this paper, a Liouville type theorem saying that if maxN−4s−2a,0<α- Published
- 2024
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