Uniqueness and nondegeneracy of ground states for −Δu+u=(Iα⋆u2)u-Δ u+u=\left({{\rm{I}}}_{α }\star {u}^{2})u in R3{{\mathbb{R}}}^{3} when αα is close to 2 - Luo Huxiao; Zhang Dingliang; Xu Yating (Advances in Nonlinear Analysis)
In this article, we study the following Choquard equation: −Δu+u=(Iα⋆u2)u,x∈R3,-Δ u+u=\left({{\rm{I}}}_{α }\star {u}^{2})u,\hspace{1.0em}x\in {{\mathbb{R}}}^{3}, where Iα{{\rm{I}}}_{α } is the Riesz potential and αα is sufficiently close to 2. By investigating the limit profile of ground states of the equation as α→2α → 2, we prove the uniqueness and nondegeneracy of ground states.