Blow-up of ground states of fractional Choquard equations. (December 2022) - Vilasi, Luca; Wang, Youjun
Abstract: We investigate the blow-up behavior of ground states of the fractional Choquard equation ( − Δ ) s u + u = ( K α ∗ | u | p ϵ ) | u | p ϵ − 2 u in  R N, with s ∈ ( 0, 1 ), N > 4 s, K α Riesz potential of order α ∈ ( 0, N ), as the exponent p ϵ approaches the upper critical growth regime in Hardy–Littlewood–Sobolev's inequality. We prove that the ground state u ϵ blows up in the sense that ‖ u ϵ ‖ L ∞ ( R N ) = o ϵ − N − 2 s 4 s as ϵ → 0 + .