Normalized ground states for a biharmonic Choquard system in ${\mathbb{R}}^4$

Abstract

In this paper, we study the existence of normalized ground state solutions for the following biharmonic Choquard system \begin{align*} \begin{split} \left\{ \begin{array}{ll} Δ^2u=λ_1 u+(I_μ*F(u,v))F_u (u,v), \quad\mbox{in}\ \ \mathbb{R}^4, Δ^2v=λ_2 v+(I_μ*F(u,v)) F_v(u,v), \quad\mbox{in}\ \ \mathbb{R}^4, \displaystyle\int_{\mathbb{R}^4}|u|^2dx=a^2,\quad \displaystyle\int_{\mathbb{R}^4}|v|^2dx=b^2,\quad u,v\in H^2(\mathbb{R}^4), \end{array} \right. \end{split} \end{align*} where $a,b>0$ are prescribed, ${\lambda }_1,{\lambda }_2\in \mathbb{R}$, $I_{\mu }=\frac{1}{|x{|}^{\mu }}$ with $\mu \in (0,4)$, $F_u,F_v$ are partial derivatives of $F$ and $F_u,F_v$ have exponential subcritical or critical growth in the sense of the Adams inequality. By using a minimax principle and analyzing the behavior of the ground state energy with respect to the prescribed mass, we obtain the existence of ground state solutions for the above problem.

arXiv admin note: text overlap with arXiv:2211.13701