Exact Asymptotic Behavior of Singular Positive Solutions of Fractional Semi-Linear Elliptic Equations

Abstract

In this paper, we prove the exact asymptotic behavior of singular positive solutions of fractional semi-linear equations $$(-\Delta {)}^{\sigma }u=u^{p}in{B}_1\backslash \{0\}$$ with an isolated singularity, where $\sigma \in (0,1)$ and $\frac{n}{n-2\sigma }<p<\frac{n+2\sigma }{n-2\sigma }$.

11 pages