A priori estimates, uniqueness and non-degeneracy of positive solutions of the Choquard equation

Zexing Li

We consider the positive solutions for the nonlocal Choquard equation $-\Delta u+u-(|\cdot {|}^{-\alpha }\ast |u{|}^p)|u{|}^{p-2}u=0$ in ${\mathbb{R}}^d$. Compared with ground states, positive s…