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arXiv · 1606.05668

Odd symmetry of least energy nodal solutions for the Choquard equation

David Ruiz·Jean Van Schaftingen
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Abstract

We consider the Choquard equation (also known as stationary Hartree equation or Schrödinger--Newton equation) \[ -Δu + u = (I_α\star |u|^p) |u|^{p - 2}u. \] Here $I_α$ stands for the Riesz potential of order $α\in (0,N)$, and $\frac{N - 2}{N + α} < \frac{1}{p} \le \frac{1}{2}$. We prove that least energy nodal solutions have an odd symmetry with respect to a hyperplane when $α$ is either close to $0$ or close to $N$.

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David Ruiz, Jean Van Schaftingen. 2016-06-17. Odd symmetry of least energy nodal solutions for the Choquard equation. https://doi.org/10.1016/j.jde.2017.09.034

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