Limit profiles and uniqueness of ground states to the nonlinear Choquard equations

Abstract

Consider nonlinear Choquard equations (equations presented) where I α denotes the Riesz potential and α ϵ (0, N). In this paper, we investigate limit profiles of ground states of nonlinear Choquard equations as α → 0 or α → N. This leads to the uniqueness and nondegeneracy of ground states when α is sufficiently close to 0 or close to N.