Can I read Limit profiles and uniqueness of ground states to the nonlinear Choquard equations on EtoBox?

Limit profiles and uniqueness of ground states to the nonlinear Choquard equations by Seok, Jinmyoung is a scholarly article available to read on EtoBox.

What is Limit profiles and uniqueness of ground states to the nonlinear Choquard equations about?

Consider nonlinear Choquard equations \begin{equation*} \left\{\begin{array}{rcl} -\Delta u +u & = &(I_\alpha*|u|^p)|u|^{p-2}u \quad \text{in } \mathbb{R}^N, \\ \lim_{x \to \infty}u(x) & = &0, \end{array}\right. \end{equation*} where $I_\alpha$ denotes Riesz potential and $\alpha \in (0, N)$. In this paper, we investigate limit profiles of ground states of nonlinear Choquard equations as $\alpha \to 0$ or $\alpha \to N$. This leads to the uniqueness and nondegeneracy of ground states when $\alpha$ is sufficiently close to $0$ or close to $N$.

Author

Seok, Jinmyoung

Published

2017

Language

EN