Liouville theorem and classification of positive solutions for a fractional Choquard type equation. (August 2019) - Le, Phuong
Abstract: Let n ≥ 2, 0 < α < 2 and 0 < β < n . We prove that the equation ( − Δ ) α 2 u = 1 | x | n − β ∗ u p u p − 1 in R n has no positive solution if 1 ≤ p < n + β n − α . We also classify all positive solutions to the equation in the critical case p = n + β n − α .