A Liouville type theorem for fractional elliptic equation with exponential nonlinearity

Anh Tuan Duong; Van Hoang Nguyen

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arXiv · 1911.05966

A Liouville type theorem for fractional elliptic equation with exponential nonlinearity

Anh Tuan Duong·Van Hoang Nguyen

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Abstract

In this paper, we are concerned with stable solutions to the fractional elliptic equation $$ (-\Delta)^s u=e^u\mbox{ in }\mathbb R^{N}, $$ where $(-\Delta)^s$ is the fractional Laplacian with $0<s<1$. We establish the nonexistence of stable solutions provided that $N<10s$. This result is optimal when $s\uparrow 1$.

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Anh Tuan Duong, Van Hoang Nguyen. 2019-11-14. A Liouville type theorem for fractional elliptic equation with exponential nonlinearity. https://arxiv.org/abs/1911.05966

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