论文标题
Biharmonic Choquard方程的归一化解决方案，其指数临界增长为$ \ Mathbb {r}^4 $
Normalized solutions for a biharmonic Choquard equation with exponential critical growth in $\mathbb{R}^4$
论文作者
论文摘要
在本文中，我们研究以下Biharmonic Choquard类型方程\ Begin {Align*} \ begin {split} \左边\{ \ begin {array} {ll} γδ^2U-βΔU=λu+（i_μ*f（u））f（u）， \ quad \ mbox {in} \ displaystyle \ int _ {\ mathbb {r}^4} | u |^2dx = c^2> 0，\ quad u \ in H^2（\ Mathbb {r}^4）， \ end {array} \正确的。 \ end {split} \ end {align*}其中$γ> 0 $，$β\ geq0 $，$λ\ in \ mathbb {r} $，$i_μ= \ frac {1} {| x | x |^μ} $带有$μ 生长。当非线性$ f $满足某些条件时，我们可以证明上述问题的基础状态标准化解决方案。
In this paper, we study the following biharmonic Choquard type equation \begin{align*} \begin{split} \left\{ \begin{array}{ll} γΔ^2u-βΔu=λu+(I_μ*F(u))f(u), \quad\mbox{in}\ \ \mathbb{R}^4, \displaystyle\int_{\mathbb{R}^4}|u|^2dx=c^2>0,\quad u\in H^2(\mathbb{R}^4), \end{array} \right. \end{split} \end{align*} where $γ>0$, $β\geq0$, $λ\in \mathbb{R}$, $I_μ=\frac{1}{|x|^μ}$ with $μ\in (0,4)$, $F(u)$ is the primitive function of $f(u)$, and $f$ is a continuous function with exponential critical growth. We can prove the existence of ground state normalized solutions for the above problem when the nonlinearity $f$ satisfies some conditions.
