Existence of ground state solutions to Kirchhoff--Choquard system in $\mathbb{R}^3$ with nonconstant potentials
Year: 2026
Type: preprint
Abstract: In this paper, we study the following linearly coupled Kirchhoff-Choquard system in $\mathbb{R}^3$: \begin{align*}\left\{\begin{array}{l} &-\left(a_1+b_1\int_{\mathbb{R}^3}|\nabla u|^2\,dx\right)Δu+V_1(x)u=μ(I_α*|u|^p)|u|^{p-2}u+λv,\quad x \in \mathbb{R}^3,\cr &-\left(a_2+b_2\int_{\mathbb{R}^3}|\nabla v|^2\,dx\right)Δv+V_2(x)v=ν(I_α*|v|^q)|v|^{q-2}v+λu,\quad x \in \mathbb{R}^3,\cr &u, v \in H^1(\mathbb{R}^3), \end{array}\right. \end{align*} where $a_1, a_2, b_1, b_2, λ, μ,$ and $ν$ are positive constants. When the potentials are constant functions, the author previously proved the existence of positive ground state solutions in the following cases: the noncritical case $\frac{3+α}{3}
Source: arXiv (Cornell University)
Author: Matsuzawa, Hiroshi
Institution: Kanagawa University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213495389