Sharp blow up estimates and precise asymptotic behavior of singular positive solutions to fractional Hardy-Hénon equations

In this paper, we study the asymptotic behavior of positive solutions fractional Hardy-Hénon equation ( ? ? ) ? u = | x ? p in B 1 \ { 0 } with an isolated singularity at origin, where ? , and punctured unit ball ? R n ? 2 . When < + give a classification singularities solutions, particular, implies sharp blow up estimates singular solutions. Further, describe precise near singularity. More generally, classify boundary for relevant degenerate elliptic nonlinear Neumann condition. These results parallel those known Laplacian counterpart proved by Gidas Spruck (1981) [21] but methods are very different, since ODEs analysis is missing ingredient case. Our proofs based on monotonicity formula, combined (down) arguments, Kelvin transformation uniqueness related equations S We also investigate located infinity equations.