论文标题
通过本地pohožaev身份构建无限的许多解决方案，以实现关键的choquard方程
Construction of infinitely many solutions for a critical Choquard equation via local Pohožaev identities
论文作者
论文摘要
在本文中，我们研究了具有轴对称电势的一类关键ch虫方程， $$ -ΔU+ v（| x'|，x''）u = \ big（| x |^{ - 4} \ ast | u |^{2} \ big） $$ 其中$（x'，x''）\ in \ mathbb {r}^2 \ times \ times \ mathbb {r}^{4} $，$ v（| x'|，x'''）$是$ \ mathbb {r}^{r}^{r}^{+times \ times \ mathbb =卷积。在强壮的小木 - 贝布尔特不等式的意义上，该方程至关重要。通过应用有限的尺寸缩小参数并开发新的本地pohožaev身份，我们证明，如果函数$ r^2v（r，x''''）$具有拓扑上的非平凡临界点，那么问题就可以接受无限的许多解决方案，该解决方案具有任意大能量。
In this paper, we study a class of the critical Choquard equations with axisymmetric potentials, $$ -Δu+ V(|x'|,x'')u =\Big(|x|^{-4}\ast |u|^{2}\Big)u\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathbb{R}^6, $$ where $(x',x'')\in \mathbb{R}^2\times\mathbb{R}^{4}$, $V(|x'|, x'')$ is a bounded nonnegative function in $\mathbb{R}^{+}\times\mathbb{R}^{4}$, and $*$ stands for the standard convolution. The equation is critical in the sense of the Hardy-Littlewood-Sobolev inequality. By applying a finite dimensional reduction argument and developing novel local Pohožaev identities, we prove that if the function $r^2V(r,x'')$ has a topologically nontrivial critical point then the problem admits infinitely many solutions with arbitrary large energies.
