Normalized ground states for a kind of Choquard–Kirchhoff equations with critical nonlinearities
Year: 2024
Type: article
Abstract: In this paper, we consider the existence of a normalized ground-state solution for the Choquard–Kirchhoff equation: $$ \left \{ \textstyle\begin{array}{l@{\quad}r} -(a+b\int _{\mathbb{R}^{3}}|\nabla u|^{2}dx)\Delta{u}=\lambda u+\mu (I_{ \alpha}\ast |u|^{p})|u|^{p-2}u+\omega |u|^{4}u,\ \ &\text{in}\, \mathbb{R}^{3}, \\ u>0,\quad \int _{\mathbb{R}^{3}}|u|^{2}=m^{2},\,&\text{in}\, \mathbb{R}^{3}, \end{array}\displaystyle \right . $$ where a, b, m, μ, $\omega >0$ , $p\in (2,\frac{7+\alpha}{3})$ , $\lambda \in \mathbb{R}$ , $\alpha \in (0,3)$ , and $I_{\alpha}$ is a Riesz potential. Utilizing approximation methods and Schwartz symmetrization rearrangements, we establish the existence of normalized ground states for these kinds of mass-constrained Choquard–Kirchhoff problems.
Source: Boundary Value Problems
Authors: Jiayi Fei, Qiongfen Zhang
Institution: Guilin University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,790
OpenAlex ID: W4403828139