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arXiv · 2210.14513

Normalized solutions for the Choquard equation with mass supercritical nonlinearity

Na Xu·Shiwang Ma
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Abstract

We consider the nonlinear Choquard equation $$\begin{cases} & - Δu = (I_α\ast F(u))F'(u) -μu \ \text{in}\ \mathbb{R}^N, & u \in \ H^1(\mathbb{R}^N), \ \int_{\mathbb{R}^N} |u|^2 dx=m, \end{cases} $$ where $α\in(0,N)$, $m>0$ is prescribed, $μ\in \mathbb{R}$ is a Lagarange multiplier, and $I_α$ is the Riesz potential. Under general assumptions on the nonlinearity $F,$ we prove the existence and multiplicity of normalized solutions.

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Na Xu, Shiwang Ma. 2022-12-27. Normalized solutions for the Choquard equation with mass supercritical nonlinearity. https://arxiv.org/abs/2210.14513

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