论文标题
Biharmonic Choquard方程的标准化基态，其指数临界增长
Normalized ground states for a biharmonic Choquard equation with exponential critical growth
论文作者
论文摘要
在本文中，我们考虑了以下Biharmonic Choquard类型问题的归一化基态解决方案\ begin {align*} \ begin {split} \左边\{ \ begin {array} {ll} δ^2U-βΔU=λu+（i_μ*f（u））f（u）， \ quad \ mbox {in} \ displaystyle \ int _ {\ mathbb {r}^4} | u |^2dx = c^2，\ quad u \ in H^2（\ Mathbb {r}^4），， \ end {array} \正确的。 \ end {split} \ end {align*}其中$β\ geq0 $，$ c> 0 $，$λ\ in \ mathbb {r} $，$i_μ= \ frac {1} {| x |^μ} $带有$μ从亚当斯不平等的意义上讲。通过使用基于同质稳定家族的最小原理，我们获得上述问题至少可以接受一个基态归一化解决方案。
In this paper, we consider the normalized ground state solution for the following biharmonic Choquard type problem \begin{align*} \begin{split} \left\{ \begin{array}{ll} Δ^2u-βΔu=λu+(I_μ*F(u))f(u), \quad\mbox{in}\ \ \mathbb{R}^4, \displaystyle\int_{\mathbb{R}^4}|u|^2dx=c^2,\quad u\in H^2(\mathbb{R}^4), \end{array} \right. \end{split} \end{align*} where $β\geq0$, $c>0$, $λ\in \mathbb{R}$, $I_μ=\frac{1}{|x|^μ}$ with $μ\in (0,4)$, $F(u)$ is the primitive function of $f(u)$, and $f$ is a continuous function with exponential critical growth in the sense of the Adams inequality. By using a minimax principle based on the homotopy stable family, we obtain that the above problem admits at least one ground state normalized solution.
