Normalized solutions for the Choquard equation with potential and combined nonlinearities
Abstract
Abstract In this paper, we study multiple normalized solutions for the following Choquard equation: − Δ u + V ( x ) u + λ u = μ I α ∗ | u | p u p − 2 u + | u | 2 * − 2 u , in R N , ∫ R N | u | 2 = a > 0 , $$\begin{cases}-{\Delta}u+V\left(x\right)u+\lambda u=\mu \left({I}_{\alpha }\ast \vert u{\vert }^{p}\right){u}^{p-2}u+\vert u{\vert }^{{2}^{{\ast}}-2}u,\quad \text{in\,}{\mathbb{R}}^{N},\hfill \\ {\int }_{{\mathbb{R}}^{N}}\vert u{\vert }^{2}=a{ >}0,\hfill \end{cases}$$ where N ⩾ 3, α ∈ (0, N ), p ∈ 1 + α N − 2 , 2 α * $p\in \left(1+\frac{\alpha }{N-2},{2}_{\alpha }^{{\ast}}\right)$ , I
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Advances in Nonlinear Analysis
- Publisher
- Walter de Gruyter GmbH
- Volume
- 15
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN